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

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

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

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

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

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

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

Solving
-3 + -2x + x2 = 12

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 5}