Solve 8x(3x+5)=0

$$8 x ( 3 x + 5 ) = 0$$

Solve for x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 8x by 3x+5.

$$24x^{2}+40x=0$$

Factor out x.

$$x\left(24x+40\right)=0$$

To find equation solutions, solve x=0 and 24x+40=0.

$$x=0 x=-\frac{5}{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 8x by 3x+5.

$$24x^{2}+40x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 24 for a, 40 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-40±\sqrt{40^{2}}}{2\times 24}$$

Take the square root of 40^{2}.

$$x=\frac{-40±40}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{-40±40}{48}$$

Now solve the equation x=\frac{-40±40}{48} when ± is plus. Add -40 to 40.

$$x=\frac{0}{48}$$

Divide 0 by 48.

$$x=0$$

Now solve the equation x=\frac{-40±40}{48} when ± is minus. Subtract 40 from -40.

$$x=-\frac{80}{48}$$

Reduce the fraction \frac{-80}{48} to lowest terms by extracting and canceling out 16.

$$x=-\frac{5}{3}$$

The equation is now solved.

$$x=0 x=-\frac{5}{3}$$

Steps for Completing the Square

Use the distributive property to multiply 8x by 3x+5.

$$24x^{2}+40x=0$$

Divide both sides by 24.

$$\frac{24x^{2}+40x}{24}=\frac{0}{24}$$

Dividing by 24 undoes the multiplication by 24.

$$x^{2}+\frac{40}{24}x=\frac{0}{24}$$

Reduce the fraction \frac{40}{24} to lowest terms by extracting and canceling out 8.

$$x^{2}+\frac{5}{3}x=\frac{0}{24}$$

Divide 0 by 24.

$$x^{2}+\frac{5}{3}x=0$$

Divide \frac{5}{3}, the coefficient of the x term, by 2 to get \frac{5}{6}. Then add the square of \frac{5}{6} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{5}{3}x+\left(\frac{5}{6}\right)^{2}=\left(\frac{5}{6}\right)^{2}$$

Square \frac{5}{6} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}$$

Factor x^{2}+\frac{5}{3}x+\frac{25}{36}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{6}\right)^{2}=\frac{25}{36}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Simplify.

$$x+\frac{5}{6}=\frac{5}{6} x+\frac{5}{6}=-\frac{5}{6}$$

Subtract \frac{5}{6} from both sides of the equation.

$$x=0 x=-\frac{5}{3}$$