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

Aug 16, 2015

The solutions are
 color(blue)(x=3/2

 color(blue)(x=2

#### Explanation:

2x^2−7x+6=0

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot 6 = 12$
AND
${N}_{1} + {N}_{2} = b = - 7$

After trying out a few numbers we get ${N}_{1} = - 3$ and ${N}_{2} = - 4$
$- 3 \cdot - 4 = 12$, and $- 3 + \left(- 4\right) = - 7$

2x^2−7x+6=0 =2x^2−4x-3x+6

$2 x \left(x - 2\right) - 3 \left(x - 2\right) = 0$

$\left(2 x - 3\right) \left(x - 2\right) = 0$

Now we equate the factors to zero and obtain solutions.
2x-3 =0, color(blue)(x=3/2

x-2 =0, color(blue)(x=2