f(x)x^5-2x+3g(x)=3f(x)-2

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Solution for f(x)x^5-2x+3g(x)=3f(x)-2 equation: 


Simplifying
f(x) * x5 + -2x + 3g(x) = 3f(x) + -2

Multiply f * x
fx * x5 + -2x + 3g(x) = 3f(x) + -2

Multiply fx * x5
fx6 + -2x + 3g(x) = 3f(x) + -2

Multiply g * x
fx6 + -2x + 3gx = 3f(x) + -2

Reorder the terms:
fx6 + 3gx + -2x = 3f(x) + -2

Multiply f * x
fx6 + 3gx + -2x = 3fx + -2

Reorder the terms:
fx6 + 3gx + -2x = -2 + 3fx

Solving
fx6 + 3gx + -2x = -2 + 3fx

Solving for variable 'f'.

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

Add '-3fx' to each side of the equation.
fx6 + 3gx + -3fx + -2x = -2 + 3fx + -3fx

Reorder the terms:
-3fx + fx6 + 3gx + -2x = -2 + 3fx + -3fx

Combine like terms: 3fx + -3fx = 0
-3fx + fx6 + 3gx + -2x = -2 + 0
-3fx + fx6 + 3gx + -2x = -2

Add '-3gx' to each side of the equation.
-3fx + fx6 + 3gx + -3gx + -2x = -2 + -3gx

Combine like terms: 3gx + -3gx = 0
-3fx + fx6 + 0 + -2x = -2 + -3gx
-3fx + fx6 + -2x = -2 + -3gx

Add '2x' to each side of the equation.
-3fx + fx6 + -2x + 2x = -2 + -3gx + 2x

Combine like terms: -2x + 2x = 0
-3fx + fx6 + 0 = -2 + -3gx + 2x
-3fx + fx6 = -2 + -3gx + 2x

Reorder the terms:
2 + -3fx + fx6 + 3gx + -2x = -2 + -3gx + 2x + 2 + 3gx + -2x

Reorder the terms:
2 + -3fx + fx6 + 3gx + -2x = -2 + 2 + -3gx + 3gx + 2x + -2x

Combine like terms: -2 + 2 = 0
2 + -3fx + fx6 + 3gx + -2x = 0 + -3gx + 3gx + 2x + -2x
2 + -3fx + fx6 + 3gx + -2x = -3gx + 3gx + 2x + -2x

Combine like terms: -3gx + 3gx = 0
2 + -3fx + fx6 + 3gx + -2x = 0 + 2x + -2x
2 + -3fx + fx6 + 3gx + -2x = 2x + -2x

Combine like terms: 2x + -2x = 0
2 + -3fx + fx6 + 3gx + -2x = 0

The solution to this equation could not be determined.

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