Solve for x 3x(x-2)=12x

$3 x (x - 2) = 12 x$

Simplify $3 x (x - 2)$ .

Start simplifying.

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

Simplify by adding zeros.

$3 x (x - 2) = 12 x$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 = 12 x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 = 12 x$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 2 = 12 x$

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x = 12 x$

Move all terms containing $x$ to the left side of the equation.

Subtract $12 x$ from both sides of the equation.

$3 x^{2} - 6 x - 12 x = 0$

Subtract $12 x$ from $- 6 x$ .

$3 x^{2} - 18 x = 0$

Factor $3 x$ out of $3 x^{2} - 18 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$3 x (x) - 18 x = 0$

Factor $3 x$ out of $- 18 x$ .

$3 x (x) + 3 x (- 6) = 0$

Factor $3 x$ out of $3 x (x) + 3 x (- 6)$ .

$3 x (x - 6) = 0$

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

$x = 0$

$x - 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

The final solution is all the values that make $3 x (x - 6) = 0$ true.

$x = 0, 6$