(x+2)(x+1)+(x-2)(x+1)=4

Solution for (x+2)(x+1)+(x-2)(x+1)=4 equation:

Simplifying
(x + 2)(x + 1) + (x + -2)(x + 1) = 4

Reorder the terms:
(2 + x)(x + 1) + (x + -2)(x + 1) = 4

Reorder the terms:
(2 + x)(1 + x) + (x + -2)(x + 1) = 4

Multiply (2 + x) * (1 + x)
(2(1 + x) + x(1 + x)) + (x + -2)(x + 1) = 4
((1 * 2 + x * 2) + x(1 + x)) + (x + -2)(x + 1) = 4
((2 + 2x) + x(1 + x)) + (x + -2)(x + 1) = 4
(2 + 2x + (1 * x + x * x)) + (x + -2)(x + 1) = 4
(2 + 2x + (1x + x2)) + (x + -2)(x + 1) = 4

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) + (x + -2)(x + 1) = 4

Reorder the terms:
2 + 3x + x2 + (-2 + x)(x + 1) = 4

Reorder the terms:
2 + 3x + x2 + (-2 + x)(1 + x) = 4

Multiply (-2 + x) * (1 + x)
2 + 3x + x2 + (-2(1 + x) + x(1 + x)) = 4
2 + 3x + x2 + ((1 * -2 + x * -2) + x(1 + x)) = 4
2 + 3x + x2 + ((-2 + -2x) + x(1 + x)) = 4
2 + 3x + x2 + (-2 + -2x + (1 * x + x * x)) = 4
2 + 3x + x2 + (-2 + -2x + (1x + x2)) = 4

Combine like terms: -2x + 1x = -1x
2 + 3x + x2 + (-2 + -1x + x2) = 4

Reorder the terms:
2 + -2 + 3x + -1x + x2 + x2 = 4

Combine like terms: 2 + -2 = 0
0 + 3x + -1x + x2 + x2 = 4
3x + -1x + x2 + x2 = 4

Combine like terms: 3x + -1x = 2x
2x + x2 + x2 = 4

Combine like terms: x2 + x2 = 2x2
2x + 2x2 = 4

Solving
2x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 2x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 2x + 2x2 = 0

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

Factor a trinomial.
2((-2 + -1x)(1 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-2, 1}