Solve 2b(4b+5)=0

$$2 b ( 4 b + 5 ) = 0$$

Solve for b

$$b = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

$$b=0$$

Steps Using Factoring

Use the distributive property to multiply 2b by 4b+5.

$$8b^{2}+10b=0$$

Factor out b.

$$b\left(8b+10\right)=0$$

To find equation solutions, solve b=0 and 8b+10=0.

$$b=0 b=-\frac{5}{4}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2b by 4b+5.

$$8b^{2}+10b=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-10±\sqrt{10^{2}}}{2\times 8}$$

Take the square root of 10^{2}.

$$b=\frac{-10±10}{2\times 8}$$

Multiply 2 times 8.

$$b=\frac{-10±10}{16}$$

Now solve the equation b=\frac{-10±10}{16} when ± is plus. Add -10 to 10.

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

Divide 0 by 16.

$$b=0$$

Now solve the equation b=\frac{-10±10}{16} when ± is minus. Subtract 10 from -10.

$$b=-\frac{20}{16}$$

Reduce the fraction \frac{-20}{16} to lowest terms by extracting and canceling out 4.

$$b=-\frac{5}{4}$$

The equation is now solved.

$$b=0 b=-\frac{5}{4}$$

Steps for Completing the Square

Use the distributive property to multiply 2b by 4b+5.

$$8b^{2}+10b=0$$

Divide both sides by 8.

$$\frac{8b^{2}+10b}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$b^{2}+\frac{10}{8}b=\frac{0}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$b^{2}+\frac{5}{4}b=\frac{0}{8}$$

Divide 0 by 8.

$$b^{2}+\frac{5}{4}b=0$$

Divide \frac{5}{4}, the coefficient of the x term, by 2 to get \frac{5}{8}. Then add the square of \frac{5}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$b^{2}+\frac{5}{4}b+\left(\frac{5}{8}\right)^{2}=\left(\frac{5}{8}\right)^{2}$$

Square \frac{5}{8} by squaring both the numerator and the denominator of the fraction.

$$b^{2}+\frac{5}{4}b+\frac{25}{64}=\frac{25}{64}$$

Factor b^{2}+\frac{5}{4}b+\frac{25}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(b+\frac{5}{8}\right)^{2}=\frac{25}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(b+\frac{5}{8}\right)^{2}}=\sqrt{\frac{25}{64}}$$

Simplify.

$$b+\frac{5}{8}=\frac{5}{8} b+\frac{5}{8}=-\frac{5}{8}$$

Subtract \frac{5}{8} from both sides of the equation.

$$b=0 b=-\frac{5}{4}$$