(x^3+7x^2+11x+2)=(x+2)

Solution for (x^3+7x^2+11x+2)=(x+2) equation:

Simplifying
(x3 + 7x2 + 11x + 2) = (x + 2)

Reorder the terms:
(2 + 11x + 7x2 + x3) = (x + 2)

Remove parenthesis around (2 + 11x + 7x2 + x3)
2 + 11x + 7x2 + x3 = (x + 2)

Reorder the terms:
2 + 11x + 7x2 + x3 = (2 + x)

Remove parenthesis around (2 + x)
2 + 11x + 7x2 + x3 = 2 + x

Add '-2' to each side of the equation.
2 + 11x + 7x2 + -2 + x3 = 2 + -2 + x

Reorder the terms:
2 + -2 + 11x + 7x2 + x3 = 2 + -2 + x

Combine like terms: 2 + -2 = 0
0 + 11x + 7x2 + x3 = 2 + -2 + x
11x + 7x2 + x3 = 2 + -2 + x

Combine like terms: 2 + -2 = 0
11x + 7x2 + x3 = 0 + x
11x + 7x2 + x3 = x

Solving
11x + 7x2 + x3 = x

Solving for variable 'x'.

Reorder the terms:
11x + -1x + 7x2 + x3 = x + -1x

Combine like terms: 11x + -1x = 10x
10x + 7x2 + x3 = x + -1x

Combine like terms: x + -1x = 0
10x + 7x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + 7x + x2) = 0

Factor a trinomial.
x((5 + x)(2 + x)) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -5, -2}