(x+3)(x+2)-12=0

Solution for (x+3)(x+2)-12=0 equation:

Simplifying
(x + 3)(x + 2) + -12 = 0

Reorder the terms:
(3 + x)(x + 2) + -12 = 0

Reorder the terms:
(3 + x)(2 + x) + -12 = 0

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) + -12 = 0
((2 * 3 + x * 3) + x(2 + x)) + -12 = 0
((6 + 3x) + x(2 + x)) + -12 = 0
(6 + 3x + (2 * x + x * x)) + -12 = 0
(6 + 3x + (2x + x2)) + -12 = 0

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) + -12 = 0

Reorder the terms:
6 + -12 + 5x + x2 = 0

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

Solving
-6 + 5x + x2 = 0

Solving for variable 'x'.

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}