F(5x)=x^2+x

Solution for F(5x)=x^2+x equation:

Simplifying
F(5x) = x2 + x

Remove parenthesis around (5x)
F * 5x = x2 + x

Reorder the terms for easier multiplication:
5F * x = x2 + x

Multiply F * x
5xF = x2 + x

Reorder the terms:
5xF = x + x2

Solving
5xF = x + x2

Solving for variable 'x'.

Reorder the terms:
-1x + 5xF + -1x2 = x + x2 + -1x + -1x2

Reorder the terms:
-1x + 5xF + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-1x + 5xF + -1x2 = 0 + x2 + -1x2
-1x + 5xF + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1x + 5xF + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 5F + -1x) = 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 '(-1 + 5F + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + 5F + -1x = 0

Solving
-1 + 5F + -1x = 0

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

Add '1' to each side of the equation.
-1 + 5F + 1 + -1x = 0 + 1

Reorder the terms:
-1 + 1 + 5F + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5F + -1x = 0 + 1
5F + -1x = 0 + 1

Combine like terms: 0 + 1 = 1
5F + -1x = 1

Add '-5F' to each side of the equation.
5F + -5F + -1x = 1 + -5F

Combine like terms: 5F + -5F = 0
0 + -1x = 1 + -5F
-1x = 1 + -5F

Divide each side by '-1'.
x = -1 + 5F

Simplifying
x = -1 + 5F
Solution
x = {0, -1 + 5F}