(x-5)(x+3)=-12

Solution for (x-5)(x+3)=-12 equation:

Simplifying
(x + -5)(x + 3) = -12

Reorder the terms:
(-5 + x)(x + 3) = -12

Reorder the terms:
(-5 + x)(3 + x) = -12

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) = -12
((3 * -5 + x * -5) + x(3 + x)) = -12
((-15 + -5x) + x(3 + x)) = -12
(-15 + -5x + (3 * x + x * x)) = -12
(-15 + -5x + (3x + x2)) = -12

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) = -12

Solving
-15 + -2x + x2 = -12

Solving for variable 'x'.

Reorder the terms:
-15 + 12 + -2x + x2 = -12 + 12

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

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

Factor a trinomial.
(-1 + -1x)(3 + -1x) = 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 '(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 = {-1, 3}