# How do you solve 6x^2 - 27x +27= 0 by factoring?

Aug 20, 2015

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

 color(blue)(x=3

#### Explanation:

6x^2−27x+27=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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 6 \cdot 27 = 162$
and
${N}_{1} + {N}_{2} = b = - 27$

After trying out a few numbers we get ${N}_{1} = - 18$ and ${N}_{2} = - 9$
$- 18 \cdot - 9 = 162$, and $\left(- 18\right) + \left(- 9\right) = - 27$

6x^2−27x+27=6x^2−18x-9x+27
$6 x \left(x - 3\right) - 9 \left(x - 3\right) = 0$

$\left(6 x - 9\right) \left(x - 3\right) = 0$ is the factorised form of the expression.

We now equate each of these factors to the R.H.S ($0$)
6x-9=0, x=9/6,color(blue)(x=3/2
x-3=0, color(blue)(x=3