Solve for x: 2x^2 + 7x + 6 = 0

Solve for x: 2x2 + 7x + 6 = 0

The first thing to do is look at the left hand side and factorise it. To do this we use the reverse of FOIL. Then when the expression is factorised, we can solve for x.

1. First find the skeleton with just x's: 

(2x       )(x        )

2. Next, find 2 numbers that mutiply to make 6, and these go at the end of the brackets. This could be 6 and 1 or  2 and 3, or -6 and -1 or -2 and -3.

Since there is a 7x term, the 2 numbers must add to 7 when one of them is multiplied by 2 - due to the 2x term (2x     ).

so (2x       3)(x      2) or (2x      2)(          3)

3. Trial and error shows us that (2x + 3)(x + 2) is the right answer. 

4. Now set each bracket respectively to 0 and solve for x. The solutions are x = -3/2 and x = -2.

And there we have the answers!

Asher C. 11 Plus Maths tutor, GCSE Maths tutor, A Level Maths tutor, ...

3 months ago

Answered by Asher, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Cesar Manuel F. 13 plus  Maths tutor, GCSE Physics tutor, GCSE Comput...
View profile
£20 /hr

Cesar Manuel F.

Degree: BSc Computer Science (Bachelors) - University College London University

Subjects offered: Maths, Physics+ 2 more


“Hello! My name is Cesar, I am originally from Perú but I currently study BSc Computer Science at University College London. I graduated Markham College with Distinction after completing my International Baccalaureate (IB) course, in w...”

Tom B. GCSE Computing tutor, GCSE Maths tutor, Mentoring HTML & CSS t...
View profile
£18 /hr

Tom B.

Degree: Electronic Engineering (Masters) - York University

Subjects offered: Maths, Computing


“Hi I'm an Electronic Engineering student at the University of York.  I love using my technical skills in order to work on creative new projects.  My specialty is software programming, which I have enjoyed at an academic and proffesion...”

Steven K. GCSE Maths tutor, A Level Maths tutor, Mentoring -Personal ...
View profile
£18 /hr

Steven K.

Degree: Material Science (Masters) - Oxford, The Queen's College University

Subjects offered: Maths, -Personal Statements-

-Personal Statements-

“I started tutoring through my father who is a maths teacher, as he would pass on requests for lessons to me. Through my A levels I tutored GCSE maths, and began to also teach physics, chemistry and biology, the other subjects i was st...”

About the author

PremiumAsher C. 11 Plus Maths tutor, GCSE Maths tutor, A Level Maths tutor, ...
View profile

Asher C.

Currently unavailable: for new students

Degree: Engineering Science (Masters) - Oxford, Keble College University

Subjects offered: Maths, Science+ 4 more

-Personal Statements-
-Oxbridge Preparation-

“Me Hello, I'm Asher! I have recently completed an MEng (4 years) in Engineering Science at Keble College, University of Oxford. My degree is all about problem solving,where I've learn to solve all types of both practical and academic ...”

You may also like...

Posts by Asher

A pot of water is heated to 100C and then placed in a room at a temperature of 18C. After 5 minutes, the pan temperature falls by 20C. Find the temperature after 10minutes.

Solve for x: 2x^2 + 7x + 6 = 0

Other GCSE Maths questions

Rationalising the denominator (Surds)

Write 825 as a product of its prime factors.

In a competition, a prize is won every 2014 seconds. Work out an estimate for the number of prizes won in 24 hours. You must show your working. (4 marks)

How do you expand brackets?

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss