# How do you solve 4x^2 + 4x - 3 = 0 by factoring?

Aug 12, 2015

The solutions for the equation are
color(blue)(x=-3/2, x=1/2

#### Explanation:

4x^2+4x−3

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 4 \cdot \left(- 3\right) = - 12$
and
${N}_{1} + {N}_{2} = b = 4$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = - 2$
$6 \cdot \left(- 2\right) = - 12$, and $6 + \left(- 2\right) = 4$

4x^2+color(blue)(4x)−3 =4x^2-color(blue)(2x +6x)−3

$= 2 x \left(2 x - 1\right) + 3 \left(2 x - 1\right)$

color(blue)((2x+3)(2x-1) is the factorised form of the expression.

Now we can equate each of the two factors to zero and find the solutions.

2x+3 = 0, color(blue)(x=-3/2
2x-1=0, color(blue)(x=1/2