(x-4)(x+8)=-27

Solution for (x-4)(x+8)=-27 equation:

Simplifying
(x + -4)(x + 8) = -27

Reorder the terms:
(-4 + x)(x + 8) = -27

Reorder the terms:
(-4 + x)(8 + x) = -27

Multiply (-4 + x) * (8 + x)
(-4(8 + x) + x(8 + x)) = -27
((8 * -4 + x * -4) + x(8 + x)) = -27
((-32 + -4x) + x(8 + x)) = -27
(-32 + -4x + (8 * x + x * x)) = -27
(-32 + -4x + (8x + x2)) = -27

Combine like terms: -4x + 8x = 4x
(-32 + 4x + x2) = -27

Solving
-32 + 4x + x2 = -27

Solving for variable 'x'.

Reorder the terms:
-32 + 27 + 4x + x2 = -27 + 27

Combine like terms: -32 + 27 = -5
-5 + 4x + x2 = -27 + 27

Combine like terms: -27 + 27 = 0
-5 + 4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -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 '(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 = {-5, 1}