# How do you solve 6x^2+48x-54=0?

May 26, 2016

$x = 1$ or $x = - 9$

#### Explanation:

In the equation $6 {x}^{2} + 48 x - 54 = 0$, as all monomials are divisible by $6$, first divide by $6$. Hence

${x}^{2} + 8 x - 9 = 0$

We can now split the middle term in to $9 x$ and $- x$ and equation becomes

${x}^{2} + 9 x - x - 9 = 0$

or $x \left(x + 9\right) - 1 \left(x + 9\right) = 0$

or $\left(x - 1\right) \left(x + 9\right) = 0$

Hence $x = 1$ or $x = - 9$