(x-1)(x+3)-12=0

Solution for (x-1)(x+3)-12=0 equation:

Simplifying
(x + -1)(x + 3) + -12 = 0

Reorder the terms:
(-1 + x)(x + 3) + -12 = 0

Reorder the terms:
(-1 + x)(3 + x) + -12 = 0

Multiply (-1 + x) * (3 + x)
(-1(3 + x) + x(3 + x)) + -12 = 0
((3 * -1 + x * -1) + x(3 + x)) + -12 = 0
((-3 + -1x) + x(3 + x)) + -12 = 0
(-3 + -1x + (3 * x + x * x)) + -12 = 0
(-3 + -1x + (3x + x2)) + -12 = 0

Combine like terms: -1x + 3x = 2x
(-3 + 2x + x2) + -12 = 0

Reorder the terms:
-3 + -12 + 2x + x2 = 0

Combine like terms: -3 + -12 = -15
-15 + 2x + x2 = 0

Solving
-15 + 2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5, 3}