8(x+4)=8x+x(x+4)

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


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

Reorder the terms:
8(4 + x) = 8x + x(x + 4)
(4 * 8 + x * 8) = 8x + x(x + 4)
(32 + 8x) = 8x + x(x + 4)

Reorder the terms:
32 + 8x = 8x + x(4 + x)
32 + 8x = 8x + (4 * x + x * x)
32 + 8x = 8x + (4x + x2)

Combine like terms: 8x + 4x = 12x
32 + 8x = 12x + x2

Solving
32 + 8x = 12x + x2

Solving for variable 'x'.

Combine like terms: 8x + -12x = -4x
32 + -4x + -1x2 = 12x + x2 + -12x + -1x2

Reorder the terms:
32 + -4x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
32 + -4x + -1x2 = 0 + x2 + -1x2
32 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
32 + -4x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(8 + x) = 0


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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

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

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

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

Simplifying
x = -8
Solution
x = {4, -8}

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