Solve for x (2x-10)(3x+12)=0

$(2 x - 10) (3 x + 12) = 0$

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

$2 x - 10 = 0$

$3 x + 12 = 0$

Set $2 x - 10$ equal to $0$ and solve for $x$ .

Set $2 x - 10$ equal to $0$ .

$2 x - 10 = 0$

Solve $2 x - 10 = 0$ for $x$ .

Add $10$ to both sides of the equation.

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

Set $3 x + 12$ equal to $0$ and solve for $x$ .

Set $3 x + 12$ equal to $0$ .

$3 x + 12 = 0$

Solve $3 x + 12 = 0$ for $x$ .

Subtract $12$ from both sides of the equation.

$3 x = - 12$

Divide each term in $3 x = - 12$ by $3$ and simplify.

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x = - 4$

The final solution is all the values that make $(2 x - 10) (3 x + 12) = 0$ true.

$x = 5, - 4$