f(x)=4x^2+5f(x+2)

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Solution for f(x)=4x^2+5f(x+2) equation: 


Simplifying
f(x) = 4x2 + 5f(x + 2)

Multiply f * x
fx = 4x2 + 5f(x + 2)

Reorder the terms:
fx = 4x2 + 5f(2 + x)
fx = 4x2 + (2 * 5f + x * 5f)
fx = 4x2 + (10f + 5fx)

Reorder the terms:
fx = 10f + 5fx + 4x2

Solving
fx = 10f + 5fx + 4x2

Solving for variable 'f'.

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

Add '-10f' to each side of the equation.
-10f + fx = 10f + 5fx + -10f + 4x2

Reorder the terms:
-10f + fx = 10f + -10f + 5fx + 4x2

Combine like terms: 10f + -10f = 0
-10f + fx = 0 + 5fx + 4x2
-10f + fx = 5fx + 4x2

Add '-5fx' to each side of the equation.
-10f + fx + -5fx = 5fx + -5fx + 4x2

Combine like terms: fx + -5fx = -4fx
-10f + -4fx = 5fx + -5fx + 4x2

Combine like terms: 5fx + -5fx = 0
-10f + -4fx = 0 + 4x2
-10f + -4fx = 4x2

Combine like terms: 4x2 + -4x2 = 0
-10f + -4fx + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5f + 2fx + 2x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(5f + 2fx + 2x2)' equal to zero and attempt to solve:

Simplifying
5f + 2fx + 2x2 = 0

Solving
5f + 2fx + 2x2 = 0

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

Add '-2x2' to each side of the equation.
5f + 2fx + 2x2 + -2x2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5f + 2fx + 0 = 0 + -2x2
5f + 2fx = 0 + -2x2
Remove the zero:
5f + 2fx = -2x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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