P(x+1)=p(x)+2x+1

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Solution for P(x+1)=p(x)+2x+1 equation: 


Simplifying
P(x + 1) = p(x) + 2x + 1

Reorder the terms:
P(1 + x) = p(x) + 2x + 1
(1 * P + x * P) = p(x) + 2x + 1
(1P + xP) = p(x) + 2x + 1

Multiply p * x
1P + xP = px + 2x + 1

Reorder the terms:
1P + xP = 1 + px + 2x

Solving
1P + xP = 1 + px + 2x

Solving for variable 'P'.

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

Reorder the terms:
-1 + 1P + -1px + -2x + xP = 1 + px + 2x + -1 + -1px + -2x

Reorder the terms:
-1 + 1P + -1px + -2x + xP = 1 + -1 + px + -1px + 2x + -2x

Combine like terms: 1 + -1 = 0
-1 + 1P + -1px + -2x + xP = 0 + px + -1px + 2x + -2x
-1 + 1P + -1px + -2x + xP = px + -1px + 2x + -2x

Combine like terms: px + -1px = 0
-1 + 1P + -1px + -2x + xP = 0 + 2x + -2x
-1 + 1P + -1px + -2x + xP = 2x + -2x

Combine like terms: 2x + -2x = 0
-1 + 1P + -1px + -2x + xP = 0

The solution to this equation could not be determined.

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