32=.5[(x+6)+(x+2)]x

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Solution for 32=.5[(x+6)+(x+2)]x equation: 


Simplifying
32 = 0.5[(x + 6) + (x + 2)] * x

Reorder the terms:
32 = 0.5[(6 + x) + (x + 2)] * x

Remove parenthesis around (6 + x)
32 = 0.5[6 + x + (x + 2)] * x

Reorder the terms:
32 = 0.5[6 + x + (2 + x)] * x

Remove parenthesis around (2 + x)
32 = 0.5[6 + x + 2 + x] * x

Reorder the terms:
32 = 0.5[6 + 2 + x + x] * x

Combine like terms: 6 + 2 = 8
32 = 0.5[8 + x + x] * x

Combine like terms: x + x = 2x
32 = 0.5[8 + 2x] * x

Reorder the terms for easier multiplication:
32 = 0.5x[8 + 2x]
32 = [8 * 0.5x + 2x * 0.5x]
32 = [4x + 1x2]

Solving
32 = 4x + 1x2

Solving for variable 'x'.

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

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

Combine like terms: 1x2 + -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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