Solve 8x(x-3)=0

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

Solve for x

$$x=3$$

$$x=0$$

Steps Using Factoring

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

$$8x^{2}-24x=0$$

Factor out x.

$$x\left(8x-24\right)=0$$

To find equation solutions, solve x=0 and 8x-24=0.

$$x=0 x=3$$

Steps Using the Quadratic Formula

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

$$8x^{2}-24x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 8}$$

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

$$x=\frac{-\left(-24\right)±24}{2\times 8}$$

The opposite of -24 is 24.

$$x=\frac{24±24}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{24±24}{16}$$

Now solve the equation x=\frac{24±24}{16} when ± is plus. Add 24 to 24.

$$x=\frac{48}{16}$$

Divide 48 by 16.

$$x=3$$

Now solve the equation x=\frac{24±24}{16} when ± is minus. Subtract 24 from 24.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

The equation is now solved.

$$x=3 x=0$$

Steps for Completing the Square

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

$$8x^{2}-24x=0$$

Divide both sides by 8.

$$\frac{8x^{2}-24x}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\left(-\frac{24}{8}\right)x=\frac{0}{8}$$

Divide -24 by 8.

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

Divide 0 by 8.

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

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{4}$$

Factor x^{2}-3x+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$x-\frac{3}{2}=\frac{3}{2} x-\frac{3}{2}=-\frac{3}{2}$$

Add \frac{3}{2} to both sides of the equation.

$$x=3 x=0$$