X^4+ax^3-3x^2-2ax+a^2=f(x)

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Solution for X^4+ax^3-3x^2-2ax+a^2=f(x) equation: 


Simplifying
X4 + ax3 + -3x2 + -2ax + a2 = f(x)

Reorder the terms:
X4 + -2ax + ax3 + a2 + -3x2 = f(x)

Multiply f * x
X4 + -2ax + ax3 + a2 + -3x2 = fx

Solving
X4 + -2ax + ax3 + a2 + -3x2 = fx

Solving for variable 'X'.

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

Add '2ax' to each side of the equation.
X4 + -2ax + ax3 + a2 + 2ax + -3x2 = 2ax + fx

Reorder the terms:
X4 + -2ax + 2ax + ax3 + a2 + -3x2 = 2ax + fx

Combine like terms: -2ax + 2ax = 0
X4 + 0 + ax3 + a2 + -3x2 = 2ax + fx
X4 + ax3 + a2 + -3x2 = 2ax + fx

Add '-1ax3' to each side of the equation.
X4 + ax3 + a2 + -1ax3 + -3x2 = 2ax + -1ax3 + fx

Reorder the terms:
X4 + ax3 + -1ax3 + a2 + -3x2 = 2ax + -1ax3 + fx

Combine like terms: ax3 + -1ax3 = 0
X4 + 0 + a2 + -3x2 = 2ax + -1ax3 + fx
X4 + a2 + -3x2 = 2ax + -1ax3 + fx

Add '-1a2' to each side of the equation.
X4 + a2 + -1a2 + -3x2 = 2ax + -1ax3 + -1a2 + fx

Combine like terms: a2 + -1a2 = 0
X4 + 0 + -3x2 = 2ax + -1ax3 + -1a2 + fx
X4 + -3x2 = 2ax + -1ax3 + -1a2 + fx

Add '3x2' to each side of the equation.
X4 + -3x2 + 3x2 = 2ax + -1ax3 + -1a2 + fx + 3x2

Combine like terms: -3x2 + 3x2 = 0
X4 + 0 = 2ax + -1ax3 + -1a2 + fx + 3x2
X4 = 2ax + -1ax3 + -1a2 + fx + 3x2

Simplifying
X4 = 2ax + -1ax3 + -1a2 + fx + 3x2

Reorder the terms:
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 2ax + -2ax + -1ax3 + ax3 + -1a2 + a2 + fx + -1fx + 3x2 + -3x2

Combine like terms: 2ax + -2ax = 0
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 0 + -1ax3 + ax3 + -1a2 + a2 + fx + -1fx + 3x2 + -3x2
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = -1ax3 + ax3 + -1a2 + a2 + fx + -1fx + 3x2 + -3x2

Combine like terms: -1ax3 + ax3 = 0
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 0 + -1a2 + a2 + fx + -1fx + 3x2 + -3x2
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = -1a2 + a2 + fx + -1fx + 3x2 + -3x2

Combine like terms: -1a2 + a2 = 0
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 0 + fx + -1fx + 3x2 + -3x2
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = fx + -1fx + 3x2 + -3x2

Combine like terms: fx + -1fx = 0
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 0 + 3x2 + -3x2
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
X4 + -2ax + ax3 + a2 + -1fx + -3x2 = 0

The solution to this equation could not be determined.

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