Solve -60pix^2+480pix+1200pi

$$-60 \pi { x }^{ 2 } +480 \pi x+1200 \pi$$

Factor

$$-60\pi \left(x-10\right)\left(x+2\right)$$

Solution Steps

Factor out 60.

$$60\left(-\pi x^{2}+8\pi x+20\pi \right)$$

Consider -\pi x^{2}+8\pi x+20\pi . Factor out \pi .

$$\pi \left(-x^{2}+8x+20\right)$$

Consider -x^{2}+8x+20. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+20. To find a and b, set up a system to be solved.

$$a+b=8 ab=-20=-20$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -20.

$$-1,20 -2,10 -4,5$$

Calculate the sum for each pair.

$$-1+20=19 -2+10=8 -4+5=1$$

The solution is the pair that gives sum 8.

$$a=10 b=-2$$

Rewrite -x^{2}+8x+20 as \left(-x^{2}+10x\right)+\left(-2x+20\right).

$$\left(-x^{2}+10x\right)+\left(-2x+20\right)$$

Factor out -x in the first and -2 in the second group.

$$-x\left(x-10\right)-2\left(x-10\right)$$

Factor out common term x-10 by using distributive property.

$$\left(x-10\right)\left(-x-2\right)$$

Rewrite the complete factored expression.

$$60\pi \left(x-10\right)\left(-x-2\right)$$

Evaluate

$$-60\pi \left(x-10\right)\left(x+2\right)$$