Solve 3x(x-8)=0

$$3 x ( x - 8 ) = 0$$

Solve for x

$$x=8$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 3x by x-8.

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

Factor out x.

$$x\left(3x-24\right)=0$$

To find equation solutions, solve x=0 and 3x-24=0.

$$x=0 x=8$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3x by x-8.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 3}$$

Take the square root of \left(-24\right)^{2}.

$$x=\frac{-\left(-24\right)±24}{2\times 3}$$

The opposite of -24 is 24.

$$x=\frac{24±24}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{24±24}{6}$$

Now solve the equation x=\frac{24±24}{6} when ± is plus. Add 24 to 24.

$$x=\frac{48}{6}$$

Divide 48 by 6.

$$x=8$$

Now solve the equation x=\frac{24±24}{6} when ± is minus. Subtract 24 from 24.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

The equation is now solved.

$$x=8 x=0$$

Steps for Completing the Square

Use the distributive property to multiply 3x by x-8.

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

Divide both sides by 3.

$$\frac{3x^{2}-24x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\left(-\frac{24}{3}\right)x=\frac{0}{3}$$

Divide -24 by 3.

$$x^{2}-8x=\frac{0}{3}$$

Divide 0 by 3.

$$x^{2}-8x=0$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}$$

Square -4.

$$x^{2}-8x+16=16$$

Factor x^{2}-8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-4\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{16}$$

Simplify.

$$x-4=4 x-4=-4$$

Add 4 to both sides of the equation.

$$x=8 x=0$$