Solve 3u^2=-15u

$$3 u ^ { 2 } = - 15 u$$

Solve for u

$$u=-5$$

$$u=0$$

Steps Using Factoring

Add 15u to both sides.

$$3u^{2}+15u=0$$

Factor out u.

$$u\left(3u+15\right)=0$$

To find equation solutions, solve u=0 and 3u+15=0.

$$u=0 u=-5$$

Steps Using the Quadratic Formula

Add 15u to both sides.

$$3u^{2}+15u=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 15 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{-15±\sqrt{15^{2}}}{2\times 3}$$

Take the square root of 15^{2}.

$$u=\frac{-15±15}{2\times 3}$$

Multiply 2 times 3.

$$u=\frac{-15±15}{6}$$

Now solve the equation u=\frac{-15±15}{6} when ± is plus. Add -15 to 15.

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

Divide 0 by 6.

$$u=0$$

Now solve the equation u=\frac{-15±15}{6} when ± is minus. Subtract 15 from -15.

$$u=-\frac{30}{6}$$

Divide -30 by 6.

$$u=-5$$

The equation is now solved.

$$u=0 u=-5$$

Steps for Completing the Square

Add 15u to both sides.

$$3u^{2}+15u=0$$

Divide both sides by 3.

$$\frac{3u^{2}+15u}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$u^{2}+\frac{15}{3}u=\frac{0}{3}$$

Divide 15 by 3.

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

Divide 0 by 3.

$$u^{2}+5u=0$$

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

$$u^{2}+5u+\left(\frac{5}{2}\right)^{2}=\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

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

Factor u^{2}+5u+\frac{25}{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}.

$$\left(u+\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(u+\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Simplify.

$$u+\frac{5}{2}=\frac{5}{2} u+\frac{5}{2}=-\frac{5}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$u=0 u=-5$$