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

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


Simplifying
x3 + 2x2 + -5x + -5 = (x + 3)(x + -2)(x + 1) + 1

Reorder the terms:
-5 + -5x + 2x2 + x3 = (x + 3)(x + -2)(x + 1) + 1

Reorder the terms:
-5 + -5x + 2x2 + x3 = (3 + x)(x + -2)(x + 1) + 1

Reorder the terms:
-5 + -5x + 2x2 + x3 = (3 + x)(-2 + x)(x + 1) + 1

Reorder the terms:
-5 + -5x + 2x2 + x3 = (3 + x)(-2 + x)(1 + x) + 1

Multiply (3 + x) * (-2 + x)
-5 + -5x + 2x2 + x3 = (3(-2 + x) + x(-2 + x))(1 + x) + 1
-5 + -5x + 2x2 + x3 = ((-2 * 3 + x * 3) + x(-2 + x))(1 + x) + 1
-5 + -5x + 2x2 + x3 = ((-6 + 3x) + x(-2 + x))(1 + x) + 1
-5 + -5x + 2x2 + x3 = (-6 + 3x + (-2 * x + x * x))(1 + x) + 1
-5 + -5x + 2x2 + x3 = (-6 + 3x + (-2x + x2))(1 + x) + 1

Combine like terms: 3x + -2x = 1x
-5 + -5x + 2x2 + x3 = (-6 + 1x + x2)(1 + x) + 1

Multiply (-6 + 1x + x2) * (1 + x)
-5 + -5x + 2x2 + x3 = (-6(1 + x) + 1x * (1 + x) + x2(1 + x)) + 1
-5 + -5x + 2x2 + x3 = ((1 * -6 + x * -6) + 1x * (1 + x) + x2(1 + x)) + 1
-5 + -5x + 2x2 + x3 = ((-6 + -6x) + 1x * (1 + x) + x2(1 + x)) + 1
-5 + -5x + 2x2 + x3 = (-6 + -6x + (1 * 1x + x * 1x) + x2(1 + x)) + 1
-5 + -5x + 2x2 + x3 = (-6 + -6x + (1x + 1x2) + x2(1 + x)) + 1
-5 + -5x + 2x2 + x3 = (-6 + -6x + 1x + 1x2 + (1 * x2 + x * x2)) + 1
-5 + -5x + 2x2 + x3 = (-6 + -6x + 1x + 1x2 + (1x2 + x3)) + 1

Combine like terms: -6x + 1x = -5x
-5 + -5x + 2x2 + x3 = (-6 + -5x + 1x2 + 1x2 + x3) + 1

Combine like terms: 1x2 + 1x2 = 2x2
-5 + -5x + 2x2 + x3 = (-6 + -5x + 2x2 + x3) + 1

Reorder the terms:
-5 + -5x + 2x2 + x3 = -6 + 1 + -5x + 2x2 + x3

Combine like terms: -6 + 1 = -5
-5 + -5x + 2x2 + x3 = -5 + -5x + 2x2 + x3

Add '5' to each side of the equation.
-5 + -5x + 2x2 + 5 + x3 = -5 + -5x + 2x2 + 5 + x3

Reorder the terms:
-5 + 5 + -5x + 2x2 + x3 = -5 + -5x + 2x2 + 5 + x3

Combine like terms: -5 + 5 = 0
0 + -5x + 2x2 + x3 = -5 + -5x + 2x2 + 5 + x3
-5x + 2x2 + x3 = -5 + -5x + 2x2 + 5 + x3

Reorder the terms:
-5x + 2x2 + x3 = -5 + 5 + -5x + 2x2 + x3

Combine like terms: -5 + 5 = 0
-5x + 2x2 + x3 = 0 + -5x + 2x2 + x3
-5x + 2x2 + x3 = -5x + 2x2 + x3

Add '5x' to each side of the equation.
-5x + 2x2 + 5x + x3 = -5x + 2x2 + 5x + x3

Reorder the terms:
-5x + 5x + 2x2 + x3 = -5x + 2x2 + 5x + x3

Combine like terms: -5x + 5x = 0
0 + 2x2 + x3 = -5x + 2x2 + 5x + x3
2x2 + x3 = -5x + 2x2 + 5x + x3

Reorder the terms:
2x2 + x3 = -5x + 5x + 2x2 + x3

Combine like terms: -5x + 5x = 0
2x2 + x3 = 0 + 2x2 + x3
2x2 + x3 = 2x2 + x3

Add '-2x2' to each side of the equation.
2x2 + -2x2 + x3 = 2x2 + -2x2 + x3

Combine like terms: 2x2 + -2x2 = 0
0 + x3 = 2x2 + -2x2 + x3
x3 = 2x2 + -2x2 + x3

Combine like terms: 2x2 + -2x2 = 0
x3 = 0 + x3
x3 = x3

Add '-1x3' to each side of the equation.
x3 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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