(x+1)(x-2)+2(x+1)=0

Solution for (x+1)(x-2)+2(x+1)=0 equation:

Simplifying
(x + 1)(x + -2) + 2(x + 1) = 0

Reorder the terms:
(1 + x)(x + -2) + 2(x + 1) = 0

Reorder the terms:
(1 + x)(-2 + x) + 2(x + 1) = 0

Multiply (1 + x) * (-2 + x)
(1(-2 + x) + x(-2 + x)) + 2(x + 1) = 0
((-2 * 1 + x * 1) + x(-2 + x)) + 2(x + 1) = 0
((-2 + 1x) + x(-2 + x)) + 2(x + 1) = 0
(-2 + 1x + (-2 * x + x * x)) + 2(x + 1) = 0
(-2 + 1x + (-2x + x2)) + 2(x + 1) = 0

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

Reorder the terms:
-2 + -1x + x2 + 2(1 + x) = 0
-2 + -1x + x2 + (1 * 2 + x * 2) = 0
-2 + -1x + x2 + (2 + 2x) = 0

Reorder the terms:
-2 + 2 + -1x + 2x + x2 = 0

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

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

Solving
1x + x2 = 0

Solving for variable 'x'.

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