Solve Using the Quadratic Formula 3x(x-2)=12x

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

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $3 x (x - 2)$ .

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 $3$ .

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

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

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

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

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

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 3$ , $b = - 18$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{18 \pm \sqrt{{(- 18)}^{2} - 4 \cdot (3 \cdot 0)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 18$ to the power of $2$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 3 \cdot 0}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 0$ .

Multiply $- 4$ by $3$ .

$x = \frac{18 \pm \sqrt{324 - 12 \cdot 0}}{2 \cdot 3}$

Multiply $- 12$ by $0$ .

$x = \frac{18 \pm \sqrt{324 + 0}}{2 \cdot 3}$

Add $324$ and $0$ .

$x = \frac{18 \pm \sqrt{324}}{2 \cdot 3}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{18 \pm \sqrt{18^{2}}}{2 \cdot 3}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{18 \pm 18}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{18 \pm 18}{6}$

Simplify $\frac{18 \pm 18}{6}$ .

$x = 3 \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 6, 0$

Solve Using the Quadratic Formula 3x(x-2)=12x

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