x+2=1+(x+1)(x+2)

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


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

Reorder the terms:
2 + x = 1 + (x + 1)(x + 2)

Reorder the terms:
2 + x = 1 + (1 + x)(x + 2)

Reorder the terms:
2 + x = 1 + (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
2 + x = 1 + (1(2 + x) + x(2 + x))
2 + x = 1 + ((2 * 1 + x * 1) + x(2 + x))
2 + x = 1 + ((2 + 1x) + x(2 + x))
2 + x = 1 + (2 + 1x + (2 * x + x * x))
2 + x = 1 + (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
2 + x = 1 + (2 + 3x + x2)

Combine like terms: 1 + 2 = 3
2 + x = 3 + 3x + x2

Solving
2 + x = 3 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
2 + -3 + x + -3x + -1x2 = 3 + 3x + x2 + -3 + -3x + -1x2

Combine like terms: 2 + -3 = -1
-1 + x + -3x + -1x2 = 3 + 3x + x2 + -3 + -3x + -1x2

Combine like terms: x + -3x = -2x
-1 + -2x + -1x2 = 3 + 3x + x2 + -3 + -3x + -1x2

Reorder the terms:
-1 + -2x + -1x2 = 3 + -3 + 3x + -3x + x2 + -1x2

Combine like terms: 3 + -3 = 0
-1 + -2x + -1x2 = 0 + 3x + -3x + x2 + -1x2
-1 + -2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-1 + -2x + -1x2 = 0 + x2 + -1x2
-1 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x + x2) = 0

Factor a trinomial.
-1((1 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-1, -1}

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