(x-2)(x+4)=-5

Solution for (x-2)(x+4)=-5 equation:

Simplifying
(x + -2)(x + 4) = -5

Reorder the terms:
(-2 + x)(x + 4) = -5

Reorder the terms:
(-2 + x)(4 + x) = -5

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) = -5
((4 * -2 + x * -2) + x(4 + x)) = -5
((-8 + -2x) + x(4 + x)) = -5
(-8 + -2x + (4 * x + x * x)) = -5
(-8 + -2x + (4x + x2)) = -5

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2) = -5

Solving
-8 + 2x + x2 = -5

Solving for variable 'x'.

Reorder the terms:
-8 + 5 + 2x + x2 = -5 + 5

Combine like terms: -8 + 5 = -3
-3 + 2x + x2 = -5 + 5

Combine like terms: -5 + 5 = 0
-3 + 2x + x2 = 0

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