(x-8)(x*x-7x-8)=x*x*x-8x*x

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Solution for (x-8)(x*x-7x-8)=x*x*x-8x*x equation: 


Simplifying
(x + -8)(x * x + -7x + -8) = x * x * x + -8x * x

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

Multiply x * x
(-8 + x)(x2 + -7x + -8) = x * x * x + -8x * x

Reorder the terms:
(-8 + x)(-8 + -7x + x2) = x * x * x + -8x * x

Multiply (-8 + x) * (-8 + -7x + x2)
(-8(-8 + -7x + x2) + x(-8 + -7x + x2)) = x * x * x + -8x * x
((-8 * -8 + -7x * -8 + x2 * -8) + x(-8 + -7x + x2)) = x * x * x + -8x * x
((64 + 56x + -8x2) + x(-8 + -7x + x2)) = x * x * x + -8x * x
(64 + 56x + -8x2 + (-8 * x + -7x * x + x2 * x)) = x * x * x + -8x * x
(64 + 56x + -8x2 + (-8x + -7x2 + x3)) = x * x * x + -8x * x

Reorder the terms:
(64 + 56x + -8x + -8x2 + -7x2 + x3) = x * x * x + -8x * x

Combine like terms: 56x + -8x = 48x
(64 + 48x + -8x2 + -7x2 + x3) = x * x * x + -8x * x

Combine like terms: -8x2 + -7x2 = -15x2
(64 + 48x + -15x2 + x3) = x * x * x + -8x * x

Multiply x * x
64 + 48x + -15x2 + x3 = x2 * x + -8x * x

Multiply x2 * x
64 + 48x + -15x2 + x3 = x3 + -8x * x

Multiply x * x
64 + 48x + -15x2 + x3 = x3 + -8x2

Reorder the terms:
64 + 48x + -15x2 + x3 = -8x2 + x3

Add '-1x3' to each side of the equation.
64 + 48x + -15x2 + x3 + -1x3 = -8x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
64 + 48x + -15x2 + 0 = -8x2 + x3 + -1x3
64 + 48x + -15x2 = -8x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
64 + 48x + -15x2 = -8x2 + 0
64 + 48x + -15x2 = -8x2

Solving
64 + 48x + -15x2 = -8x2

Solving for variable 'x'.

Combine like terms: -15x2 + 8x2 = -7x2
64 + 48x + -7x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
64 + 48x + -7x2 = 0

Factor a trinomial.
(8 + -1x)(8 + 7x) = 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 '(8 + 7x)' equal to zero and attempt to solve:

Simplifying
8 + 7x = 0

Solving
8 + 7x = 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 + 7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7x = 0 + -8
7x = 0 + -8

Combine like terms: 0 + -8 = -8
7x = -8

Divide each side by '7'.
x = -1.142857143

Simplifying
x = -1.142857143
Solution
x = {8, -1.142857143}

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