x*(x+3x)=8*(8+x+4)

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Solution for x*(x+3x)=8*(8+x+4) equation: 


Simplifying
x(x + 3x) = 8(8 + x + 4)

Combine like terms: x + 3x = 4x
x(4x) = 8(8 + x + 4)

Remove parenthesis around (4x)
x * 4x = 8(8 + x + 4)

Reorder the terms for easier multiplication:
4x * x = 8(8 + x + 4)

Multiply x * x
4x2 = 8(8 + x + 4)

Reorder the terms:
4x2 = 8(8 + 4 + x)

Combine like terms: 8 + 4 = 12
4x2 = 8(12 + x)
4x2 = (12 * 8 + x * 8)
4x2 = (96 + 8x)

Solving
4x2 = 96 + 8x

Solving for variable 'x'.

Reorder the terms:
-96 + -8x + 4x2 = 96 + 8x + -96 + -8x

Reorder the terms:
-96 + -8x + 4x2 = 96 + -96 + 8x + -8x

Combine like terms: 96 + -96 = 0
-96 + -8x + 4x2 = 0 + 8x + -8x
-96 + -8x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-96 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -2x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4, 6}

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