# How do you factorise a quadratic equation?

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Take the example 2x2 + 7x + 3 = 0

1. To factorise we need to use the general equation 'ax + bx - c = 0'   where in our case a = 2 b =7 c=3.

2. First we need to mulitply the a and c values (2*3 = 6) where we have to find two numbers that will multiply to make 'ac' (6) and add to make 'b' (7)

3. It helps to list factors that make 6 and add to make 7. An example of what these factors could be is 6 and 1. Where  '6*1 = 6' and '6 + 1 = 7'

4. We then rewrite the equation to replace b with 6 and 1: 2x+ 6x + 1x +3 = 0 and find the common factor for both half of the equation.

5. The common factor for 2x2+ 6x is 2 and thus can be written as 2x(x + 3) where the second half of the equation x + 3 remains the same (x + 3). This can be written as (2x + 3) (x + 3) = 0

6. We can check if this is correct by expanding out the brackets.

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