F(x)=50x-x^2

Solution for F(x)=50x-x^2 equation:

Simplifying
F(x) = 50x + -1x2

Multiply F * x
xF = 50x + -1x2

Solving
xF = 50x + -1x2

Solving for variable 'x'.

Reorder the terms:
-50x + xF + x2 = 50x + -1x2 + -50x + x2

Reorder the terms:
-50x + xF + x2 = 50x + -50x + -1x2 + x2

Combine like terms: 50x + -50x = 0
-50x + xF + x2 = 0 + -1x2 + x2
-50x + xF + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-50x + xF + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-50 + F + x) = 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 '(-50 + F + x)' equal to zero and attempt to solve:

Simplifying
-50 + F + x = 0

Solving
-50 + F + x = 0

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

Add '50' to each side of the equation.
-50 + F + 50 + x = 0 + 50

Reorder the terms:
-50 + 50 + F + x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + F + x = 0 + 50
F + x = 0 + 50

Combine like terms: 0 + 50 = 50
F + x = 50

Add '-1F' to each side of the equation.
F + -1F + x = 50 + -1F

Combine like terms: F + -1F = 0
0 + x = 50 + -1F
x = 50 + -1F

Simplifying
x = 50 + -1F
Solution
x = {0, 50 + -1F}