f(-2x+5)=f(2x-11)

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Solution for f(-2x+5)=f(2x-11) equation: 


Simplifying
f(-2x + 5) = f(2x + -11)

Reorder the terms:
f(5 + -2x) = f(2x + -11)
(5 * f + -2x * f) = f(2x + -11)
(5f + -2fx) = f(2x + -11)

Reorder the terms:
5f + -2fx = f(-11 + 2x)
5f + -2fx = (-11 * f + 2x * f)
5f + -2fx = (-11f + 2fx)

Solving
5f + -2fx = -11f + 2fx

Solving for variable 'f'.

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

Add '11f' to each side of the equation.
5f + 11f + -2fx = -11f + 11f + 2fx

Combine like terms: 5f + 11f = 16f
16f + -2fx = -11f + 11f + 2fx

Combine like terms: -11f + 11f = 0
16f + -2fx = 0 + 2fx
16f + -2fx = 2fx

Add '-2fx' to each side of the equation.
16f + -2fx + -2fx = 2fx + -2fx

Combine like terms: -2fx + -2fx = -4fx
16f + -4fx = 2fx + -2fx

Combine like terms: 2fx + -2fx = 0
16f + -4fx = 0

Factor out the Greatest Common Factor (GCF), '4f'.
4f(4 + -1x) = 0

Ignore the factor 4.

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

Simplifying
f = 0

Solving
f = 0

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

Simplifying
f = 0

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Add 'x' to each side of the equation.
-1x + x = -4 + x

Combine like terms: -1x + x = 0
0 = -4 + x

Simplifying
0 = -4 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
f = {0}

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