(x-3)(x+6)=-8

Solution for (x-3)(x+6)=-8 equation:

Simplifying
(x + -3)(x + 6) = -8

Reorder the terms:
(-3 + x)(x + 6) = -8

Reorder the terms:
(-3 + x)(6 + x) = -8

Multiply (-3 + x) * (6 + x)
(-3(6 + x) + x(6 + x)) = -8
((6 * -3 + x * -3) + x(6 + x)) = -8
((-18 + -3x) + x(6 + x)) = -8
(-18 + -3x + (6 * x + x * x)) = -8
(-18 + -3x + (6x + x2)) = -8

Combine like terms: -3x + 6x = 3x
(-18 + 3x + x2) = -8

Solving
-18 + 3x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-18 + 8 + 3x + x2 = -8 + 8

Combine like terms: -18 + 8 = -10
-10 + 3x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}