(x+8)(3x-7)=(7-x)(x+8)

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Solution for (x+8)(3x-7)=(7-x)(x+8) equation: 


Simplifying
(x + 8)(3x + -7) = (7 + -1x)(x + 8)

Reorder the terms:
(8 + x)(3x + -7) = (7 + -1x)(x + 8)

Reorder the terms:
(8 + x)(-7 + 3x) = (7 + -1x)(x + 8)

Multiply (8 + x) * (-7 + 3x)
(8(-7 + 3x) + x(-7 + 3x)) = (7 + -1x)(x + 8)
((-7 * 8 + 3x * 8) + x(-7 + 3x)) = (7 + -1x)(x + 8)
((-56 + 24x) + x(-7 + 3x)) = (7 + -1x)(x + 8)
(-56 + 24x + (-7 * x + 3x * x)) = (7 + -1x)(x + 8)
(-56 + 24x + (-7x + 3x2)) = (7 + -1x)(x + 8)

Combine like terms: 24x + -7x = 17x
(-56 + 17x + 3x2) = (7 + -1x)(x + 8)

Reorder the terms:
-56 + 17x + 3x2 = (7 + -1x)(8 + x)

Multiply (7 + -1x) * (8 + x)
-56 + 17x + 3x2 = (7(8 + x) + -1x * (8 + x))
-56 + 17x + 3x2 = ((8 * 7 + x * 7) + -1x * (8 + x))
-56 + 17x + 3x2 = ((56 + 7x) + -1x * (8 + x))
-56 + 17x + 3x2 = (56 + 7x + (8 * -1x + x * -1x))
-56 + 17x + 3x2 = (56 + 7x + (-8x + -1x2))

Combine like terms: 7x + -8x = -1x
-56 + 17x + 3x2 = (56 + -1x + -1x2)

Solving
-56 + 17x + 3x2 = 56 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
-56 + -56 + 17x + x + 3x2 + x2 = 56 + -1x + -1x2 + -56 + x + x2

Combine like terms: -56 + -56 = -112
-112 + 17x + x + 3x2 + x2 = 56 + -1x + -1x2 + -56 + x + x2

Combine like terms: 17x + x = 18x
-112 + 18x + 3x2 + x2 = 56 + -1x + -1x2 + -56 + x + x2

Combine like terms: 3x2 + x2 = 4x2
-112 + 18x + 4x2 = 56 + -1x + -1x2 + -56 + x + x2

Reorder the terms:
-112 + 18x + 4x2 = 56 + -56 + -1x + x + -1x2 + x2

Combine like terms: 56 + -56 = 0
-112 + 18x + 4x2 = 0 + -1x + x + -1x2 + x2
-112 + 18x + 4x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-112 + 18x + 4x2 = 0 + -1x2 + x2
-112 + 18x + 4x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-112 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + 9x + 2x2) = 0

Factor a trinomial.
2((-8 + -1x)(7 + -2x)) = 0

Ignore the factor 2.

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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-8, 3.5}

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