(x+1)(x+2)=12

Solution for (x+1)(x+2)=12 equation:

Simplifying
(x + 1)(x + 2) = 12

Reorder the terms:
(1 + x)(x + 2) = 12

Reorder the terms:
(1 + x)(2 + x) = 12

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 12
((2 * 1 + x * 1) + x(2 + x)) = 12
((2 + 1x) + x(2 + x)) = 12
(2 + 1x + (2 * x + x * x)) = 12
(2 + 1x + (2x + x2)) = 12

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 12

Solving
2 + 3x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
2 + -12 + 3x + x2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 3x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

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