# How do you solve x^3 - 10x^2 +24x = 0 ?

Apr 7, 2018

$x = 0 \mathmr{and} 4 \mathmr{and} 6$

#### Explanation:

${x}^{3} - 10 {x}^{2} + 24 x = 0$

Factor,

$x \left({x}^{2} - 10 x + 24\right) = 0$

Factor,

$x \left(x - 6\right) \left(x - 4\right) = 0$

Hence,

$x = 0 \mathmr{and} 4 \mathmr{and} 6$

Apr 7, 2018

$x = 0 , x = 4 , x = 6$

#### Explanation:

$\text{take out a "color(blue)"common factor } x$

$x \left({x}^{2} - 10 x + 24\right) = 0$

$\text{the factors of + 24 which sum to - 10 are - 4 and - 6}$

$\Rightarrow x \left(x - 4\right) \left(x - 6\right) = 0$

$\text{equate each factor to zero and solve for x}$

$\Rightarrow x = 0$

$\Rightarrow x - 4 = 0 \Rightarrow x = 4$

$x - 6 = 0 \Rightarrow x = 6$