F(x+1)=f(x)+3x(x+1)+1

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Solution for F(x+1)=f(x)+3x(x+1)+1 equation: 


Simplifying
F(x + 1) = f(x) + 3x(x + 1) + 1

Reorder the terms:
F(1 + x) = f(x) + 3x(x + 1) + 1
(1 * F + x * F) = f(x) + 3x(x + 1) + 1
(1F + xF) = f(x) + 3x(x + 1) + 1

Multiply f * x
1F + xF = fx + 3x(x + 1) + 1

Reorder the terms:
1F + xF = fx + 3x(1 + x) + 1
1F + xF = fx + (1 * 3x + x * 3x) + 1
1F + xF = fx + (3x + 3x2) + 1

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

Solving
1F + xF = 1 + fx + 3x + 3x2

Solving for variable 'F'.

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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