Solve 3h(h+2)=0

$$3 h ( h + 2 ) = 0$$

Solve for h

$$h=-2$$

$$h=0$$

Steps Using Factoring

Use the distributive property to multiply 3h by h+2.

$$3h^{2}+6h=0$$

Factor out h.

$$h\left(3h+6\right)=0$$

To find equation solutions, solve h=0 and 3h+6=0.

$$h=0 h=-2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3h by h+2.

$$3h^{2}+6h=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-6±\sqrt{6^{2}}}{2\times 3}$$

Take the square root of 6^{2}.

$$h=\frac{-6±6}{2\times 3}$$

Multiply 2 times 3.

$$h=\frac{-6±6}{6}$$

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

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

Divide 0 by 6.

$$h=0$$

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

$$h=-\frac{12}{6}$$

Divide -12 by 6.

$$h=-2$$

The equation is now solved.

$$h=0 h=-2$$

Steps for Completing the Square

Use the distributive property to multiply 3h by h+2.

$$3h^{2}+6h=0$$

Divide both sides by 3.

$$\frac{3h^{2}+6h}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$h^{2}+\frac{6}{3}h=\frac{0}{3}$$

Divide 6 by 3.

$$h^{2}+2h=\frac{0}{3}$$

Divide 0 by 3.

$$h^{2}+2h=0$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$h^{2}+2h+1^{2}=1^{2}$$

Square 1.

$$h^{2}+2h+1=1$$

Factor h^{2}+2h+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(h+1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(h+1\right)^{2}}=\sqrt{1}$$

Simplify.

$$h+1=1 h+1=-1$$

Subtract 1 from both sides of the equation.

$$h=0 h=-2$$