F(x-3)-f(x)=5x^2-2x+1

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Solution for F(x-3)-f(x)=5x^2-2x+1 equation: 


Simplifying
F(x + -3) + -1f(x) = 5x2 + -2x + 1

Reorder the terms:
F(-3 + x) + -1f(x) = 5x2 + -2x + 1
(-3 * F + x * F) + -1f(x) = 5x2 + -2x + 1
(-3F + xF) + -1f(x) = 5x2 + -2x + 1

Multiply f * x
-3F + xF + -1fx = 5x2 + -2x + 1

Reorder the terms:
-3F + -1fx + xF = 5x2 + -2x + 1

Reorder the terms:
-3F + -1fx + xF = 1 + -2x + 5x2

Solving
-3F + -1fx + xF = 1 + -2x + 5x2

Solving for variable 'F'.

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

Add 'fx' to each side of the equation.
-3F + -1fx + fx + xF = 1 + -2x + fx + 5x2

Combine like terms: -1fx + fx = 0
-3F + 0 + xF = 1 + -2x + fx + 5x2
-3F + xF = 1 + -2x + fx + 5x2

Reorder the terms:
-3F + xF = 1 + fx + -2x + 5x2

Reorder the terms:
-1 + -3F + -1fx + 2x + xF + -5x2 = 1 + fx + -2x + 5x2 + -1 + -1fx + 2x + -5x2

Reorder the terms:
-1 + -3F + -1fx + 2x + xF + -5x2 = 1 + -1 + fx + -1fx + -2x + 2x + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
-1 + -3F + -1fx + 2x + xF + -5x2 = 0 + fx + -1fx + -2x + 2x + 5x2 + -5x2
-1 + -3F + -1fx + 2x + xF + -5x2 = fx + -1fx + -2x + 2x + 5x2 + -5x2

Combine like terms: fx + -1fx = 0
-1 + -3F + -1fx + 2x + xF + -5x2 = 0 + -2x + 2x + 5x2 + -5x2
-1 + -3F + -1fx + 2x + xF + -5x2 = -2x + 2x + 5x2 + -5x2

Combine like terms: -2x + 2x = 0
-1 + -3F + -1fx + 2x + xF + -5x2 = 0 + 5x2 + -5x2
-1 + -3F + -1fx + 2x + xF + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1 + -3F + -1fx + 2x + xF + -5x2 = 0

The solution to this equation could not be determined.

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