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

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


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

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

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

Multiply (-6 + x) * (8 + x)
(-6(8 + x) + x(8 + x)) = -3(x + 8)
((8 * -6 + x * -6) + x(8 + x)) = -3(x + 8)
((-48 + -6x) + x(8 + x)) = -3(x + 8)
(-48 + -6x + (8 * x + x * x)) = -3(x + 8)
(-48 + -6x + (8x + x2)) = -3(x + 8)

Combine like terms: -6x + 8x = 2x
(-48 + 2x + x2) = -3(x + 8)

Reorder the terms:
-48 + 2x + x2 = -3(8 + x)
-48 + 2x + x2 = (8 * -3 + x * -3)
-48 + 2x + x2 = (-24 + -3x)

Solving
-48 + 2x + x2 = -24 + -3x

Solving for variable 'x'.

Reorder the terms:
-48 + 24 + 2x + 3x + x2 = -24 + -3x + 24 + 3x

Combine like terms: -48 + 24 = -24
-24 + 2x + 3x + x2 = -24 + -3x + 24 + 3x

Combine like terms: 2x + 3x = 5x
-24 + 5x + x2 = -24 + -3x + 24 + 3x

Reorder the terms:
-24 + 5x + x2 = -24 + 24 + -3x + 3x

Combine like terms: -24 + 24 = 0
-24 + 5x + x2 = 0 + -3x + 3x
-24 + 5x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-24 + 5x + x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 3}

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