Solve for x x^3-144x=0

$x^{3} - 144 x = 0$

Step 1

Factor the left side of the equation.

Factor $x$ out of $x^{3} - 144 x$ .

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} - 144 x = 0$

Factor $x$ out of $- 144 x$ .

$x \cdot x^{2} + x \cdot - 144 = 0$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 144$ .

$x (x^{2} - 144) = 0$

Rewrite $144$ as $12^{2}$ .

$x (x^{2} - 12^{2}) = 0$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 12$ .

$x ((x + 12) (x - 12)) = 0$

Remove unnecessary parentheses.

$x (x + 12) (x - 12) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 12 = 0$

$x - 12 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 5

Set $x - 12$ equal to $0$ and solve for $x$ .

Set $x - 12$ equal to $0$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

Step 6

The final solution is all the values that make $x (x + 12) (x - 12) = 0$ true.

$x = 0, - 12, 12$