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

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

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

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

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

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

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

Solving
12 = 6 + 5x + x2

Solving for variable 'x'.

Combine like terms: 12 + -6 = 6
6 + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2

Reorder the terms:
6 + -5x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
6 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
6 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
6 + -5x + -1x2 = 0 + x2 + -1x2
6 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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