f(x)=-2f(5)

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


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

Multiply f * x
fx = -2f(5)

Reorder the terms for easier multiplication:
fx = -2 * 5f

Multiply -2 * 5
fx = -10f

Solving
fx = -10f

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 + 10f

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

Factor out the Greatest Common Factor (GCF), 'f'.
f(10 + x) = 0


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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Add '-1x' to each side of the equation.
x + -1x = -10 + -1x

Combine like terms: x + -1x = 0
0 = -10 + -1x

Simplifying
0 = -10 + -1x

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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