(x+2)(x+3)=12

Solution for (x+2)(x+3)=12 equation:

Simplifying
(x + 2)(x + 3) = 12

Reorder the terms:
(2 + x)(x + 3) = 12

Reorder the terms:
(2 + x)(3 + x) = 12

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 12
((3 * 2 + x * 2) + x(3 + x)) = 12
((6 + 2x) + x(3 + x)) = 12
(6 + 2x + (3 * x + x * x)) = 12
(6 + 2x + (3x + x2)) = 12

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 12

Solving
6 + 5x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
6 + -12 + 5x + x2 = 12 + -12

Combine like terms: 6 + -12 = -6
-6 + 5x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 1}