(x-8)(3x+1)=-8(x-8)

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Solution for (x-8)(3x+1)=-8(x-8) equation: 


Simplifying
(x + -8)(3x + 1) = -8(x + -8)

Reorder the terms:
(-8 + x)(3x + 1) = -8(x + -8)

Reorder the terms:
(-8 + x)(1 + 3x) = -8(x + -8)

Multiply (-8 + x) * (1 + 3x)
(-8(1 + 3x) + x(1 + 3x)) = -8(x + -8)
((1 * -8 + 3x * -8) + x(1 + 3x)) = -8(x + -8)
((-8 + -24x) + x(1 + 3x)) = -8(x + -8)
(-8 + -24x + (1 * x + 3x * x)) = -8(x + -8)
(-8 + -24x + (1x + 3x2)) = -8(x + -8)

Combine like terms: -24x + 1x = -23x
(-8 + -23x + 3x2) = -8(x + -8)

Reorder the terms:
-8 + -23x + 3x2 = -8(-8 + x)
-8 + -23x + 3x2 = (-8 * -8 + x * -8)
-8 + -23x + 3x2 = (64 + -8x)

Solving
-8 + -23x + 3x2 = 64 + -8x

Solving for variable 'x'.

Reorder the terms:
-8 + -64 + -23x + 8x + 3x2 = 64 + -8x + -64 + 8x

Combine like terms: -8 + -64 = -72
-72 + -23x + 8x + 3x2 = 64 + -8x + -64 + 8x

Combine like terms: -23x + 8x = -15x
-72 + -15x + 3x2 = 64 + -8x + -64 + 8x

Reorder the terms:
-72 + -15x + 3x2 = 64 + -64 + -8x + 8x

Combine like terms: 64 + -64 = 0
-72 + -15x + 3x2 = 0 + -8x + 8x
-72 + -15x + 3x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-72 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -5x + x2) = 0

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

Ignore the factor 3.

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 '(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
Solution
x = {-3, 8}

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