Solve 6u^2=-18u

$$6 u ^ { 2 } = - 18 u$$

Solve for u

$$u=-3$$

$$u=0$$

Steps Using Factoring

Add 18u to both sides.

$$6u^{2}+18u=0$$

Factor out u.

$$u\left(6u+18\right)=0$$

To find equation solutions, solve u=0 and 6u+18=0.

$$u=0 u=-3$$

Steps Using the Quadratic Formula

Add 18u to both sides.

$$6u^{2}+18u=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 18 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{-18±\sqrt{18^{2}}}{2\times 6}$$

Take the square root of 18^{2}.

$$u=\frac{-18±18}{2\times 6}$$

Multiply 2 times 6.

$$u=\frac{-18±18}{12}$$

Now solve the equation u=\frac{-18±18}{12} when ± is plus. Add -18 to 18.

$$u=\frac{0}{12}$$

Divide 0 by 12.

$$u=0$$

Now solve the equation u=\frac{-18±18}{12} when ± is minus. Subtract 18 from -18.

$$u=-\frac{36}{12}$$

Divide -36 by 12.

$$u=-3$$

The equation is now solved.

$$u=0 u=-3$$

Steps for Completing the Square

Add 18u to both sides.

$$6u^{2}+18u=0$$

Divide both sides by 6.

$$\frac{6u^{2}+18u}{6}=\frac{0}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$u^{2}+\frac{18}{6}u=\frac{0}{6}$$

Divide 18 by 6.

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

Divide 0 by 6.

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

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.

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

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

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

Factor u^{2}+3u+\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}.

$$\left(u+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

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

Simplify.

$$u+\frac{3}{2}=\frac{3}{2} u+\frac{3}{2}=-\frac{3}{2}$$

Subtract \frac{3}{2} from both sides of the equation.

$$u=0 u=-3$$