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!