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

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


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

Multiply F * x
xF + -1f(x + -1) = 3x2 + -5x

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

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

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

Solving
1f + -1fx + xF = -5x + 3x2

Solving for variable 'f'.

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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