P(x)=300x-25x^2

Solution for P(x)=300x-25x^2 equation:

Simplifying
P(x) = 300x + -25x2

Multiply P * x
xP = 300x + -25x2

Solving
xP = 300x + -25x2

Solving for variable 'x'.

Reorder the terms:
-300x + xP + 25x2 = 300x + -25x2 + -300x + 25x2

Reorder the terms:
-300x + xP + 25x2 = 300x + -300x + -25x2 + 25x2

Combine like terms: 300x + -300x = 0
-300x + xP + 25x2 = 0 + -25x2 + 25x2
-300x + xP + 25x2 = -25x2 + 25x2

Combine like terms: -25x2 + 25x2 = 0
-300x + xP + 25x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-300 + P + 25x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-300 + P + 25x)' equal to zero and attempt to solve:

Simplifying
-300 + P + 25x = 0

Solving
-300 + P + 25x = 0

Move all terms containing x to the left, all other terms to the right.

Add '300' to each side of the equation.
-300 + P + 300 + 25x = 0 + 300

Reorder the terms:
-300 + 300 + P + 25x = 0 + 300

Combine like terms: -300 + 300 = 0
0 + P + 25x = 0 + 300
P + 25x = 0 + 300

Combine like terms: 0 + 300 = 300
P + 25x = 300

Add '-1P' to each side of the equation.
P + -1P + 25x = 300 + -1P

Combine like terms: P + -1P = 0
0 + 25x = 300 + -1P
25x = 300 + -1P

Divide each side by '25'.
x = 12 + -0.04P

Simplifying
x = 12 + -0.04P
Solution
x = {0, 12 + -0.04P}