Solve -18u^2+108u

$$- 18 u ^ { 2 } + 108 u$$

Factor

$$18u\left(6-u\right)$$

Solution Steps

Factor out 18.

$$18\left(-u^{2}+6u\right)$$

Consider -u^{2}+6u. Factor out u.

$$u\left(-u+6\right)$$

Rewrite the complete factored expression.

$$18u\left(-u+6\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-18u^{2}+108u=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$u=\frac{-108±\sqrt{108^{2}}}{2\left(-18\right)}$$

Take the square root of 108^{2}.

$$u=\frac{-108±108}{2\left(-18\right)}$$

Multiply 2 times -18.

$$u=\frac{-108±108}{-36}$$

Now solve the equation u=\frac{-108±108}{-36} when ± is plus. Add -108 to 108.

$$u=\frac{0}{-36}$$

Divide 0 by -36.

$$u=0$$

Now solve the equation u=\frac{-108±108}{-36} when ± is minus. Subtract 108 from -108.

$$u=-\frac{216}{-36}$$

Divide -216 by -36.

$$u=6$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and 6 for x_{2}.

$$-18u^{2}+108u=-18u\left(u-6\right)$$

Evaluate

$$18u\left(6-u\right)$$