# How do you simplify (6w ^ { 2} - w - 7) ( w ^ { 2} + 2w - 5)?

May 5, 2018

$\omega = \frac{7}{6} , - 1 , \left(\sqrt{6} - 1\right) \mathmr{and} \left(- \sqrt{6} - 1\right)$

#### Explanation:

Let $\omega$ be $x$

Assuming that this equation = 0

$\therefore$ As per the question,

$\left(6 {x}^{2} - x - 7\right) \left({x}^{2} + 2 x - 5\right)$ =0

$\left(6 {x}^{2} + 6 x - 7 x - 7\right) \left(x + \sqrt{6} + 1\right) \left(x - \sqrt{6} + 1\right)$ = 0

[6x(x + 1) -7(x + 1)][(x + sqrt6 +1)(x - sqrt6 + 1) = 0

[(6x-7)(x+1)][(x + sqrt6 +1)(x - sqrt6 + 1) = 0

$\therefore$ $x = \frac{7}{6} , - 1 , \left(\sqrt{6} - 1\right) \mathmr{and} \left(- \sqrt{6} - 1\right)$

But $x = \omega$

$\therefore$ $\omega = \frac{7}{6} , - 1 , \left(\sqrt{6} - 1\right) \mathmr{and} \left(- \sqrt{6} - 1\right)$