# How do you solve 5x^2 - 7x - 6 = 0 by factoring?

Aug 12, 2015

The solutions are

color(blue)(x=-3/5
color(blue)(x=2

#### Explanation:

5x^2−7x−6=0

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 5 \cdot - 6 = - 30$
and
${N}_{1} + {N}_{2} = b = - 7$

After trying out a few numbers we get ${N}_{1} = - 10$ and ${N}_{2} = 3$
$- 10 \cdot 3 = - 30$, and $3 + \left(- 10\right) = - 7$

5x^2−color(blue)(7x)−6= 5x^2−color(blue)(10x +3x)−6

$= 5 x \left(x - 2\right) + 3 \left(x - 2\right)$

color(blue)((5x+3)(x-2)  are the factors of the expression.

Now we equate these factors to zero and find the solutions:

5x+3 = 0 , color(blue)(x=-3/5
x-2 =0, color(blue)(x=2