Solve P(x)=xP=80x-01x^2-(500+20x)

$$P ( x ) = x P = 80 x - 01 x ^ { 2 } - ( 500 + 20 x )$$

Solve for P

$$P=60-\frac{500}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply 0 and 1 to get 0.

$$xP=80x-0x^{2}-\left(500+20x\right)$$

Anything times zero gives zero.

$$xP=80x-0-\left(500+20x\right)$$

To find the opposite of 500+20x, find the opposite of each term.

$$xP=80x-0-500-20x$$

Reorder the terms.

$$Px=-20x+80x-500$$

Combine -20x and 80x to get 60x.

$$Px=60x-500$$

The equation is in standard form.

$$xP=60x-500$$

Divide both sides by x.

$$\frac{xP}{x}=\frac{60x-500}{x}$$

Dividing by x undoes the multiplication by x.

$$P=\frac{60x-500}{x}$$

Divide 60x-500 by x.

$$P=60-\frac{500}{x}$$

Solve for x

$$x=-\frac{500}{P-60}$$

$$P\neq 60$$

Steps for Solving Linear Equation

Multiply 0 and 1 to get 0.

$$xP=80x-0x^{2}-\left(500+20x\right)$$

Anything times zero gives zero.

$$xP=80x-0-\left(500+20x\right)$$

To find the opposite of 500+20x, find the opposite of each term.

$$xP=80x-0-500-20x$$

Subtract 80x-0 from both sides.

$$xP-\left(80x-0\right)=-500-20x$$

Add 20x to both sides.

$$xP-\left(80x-0\right)+20x=-500$$

Reorder the terms.

$$Px-80x+20x=-500$$

Combine -80x and 20x to get -60x.

$$Px-60x=-500$$

Combine all terms containing x.

$$\left(P-60\right)x=-500$$

Divide both sides by P-60.

$$\frac{\left(P-60\right)x}{P-60}=-\frac{500}{P-60}$$

Dividing by P-60 undoes the multiplication by P-60.

$$x=-\frac{500}{P-60}$$