32=.5x(x+12)

Solution for 32=.5x(x+12) equation:

Simplifying
32 = 0.5x(x + 12)

Reorder the terms:
32 = 0.5x(12 + x)
32 = (12 * 0.5x + x * 0.5x)
32 = (6x + 0.5x2)

Solving
32 = 6x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
32 + -6x + -0.5x2 = 6x + -6x + 0.5x2 + -0.5x2

Combine like terms: 6x + -6x = 0
32 + -6x + -0.5x2 = 0 + 0.5x2 + -0.5x2
32 + -6x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
32 + -6x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-64 + 12x + x2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 12x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 12x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 12x + x2 = 0 + 64
12x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
12x + x2 = 64

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 64 + 36

Reorder the terms:
36 + 12x + x2 = 64 + 36

Combine like terms: 64 + 36 = 100
36 + 12x + x2 = 100

Factor a perfect square on the left side:
(x + 6)(x + 6) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(x + 6) equal to 10 and -10.

Subproblem 1
x + 6 = 10

Simplifying
x + 6 = 10

Reorder the terms:
6 + x = 10

Solving
6 + x = 10

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 10 + -6

Combine like terms: 6 + -6 = 0
0 + x = 10 + -6
x = 10 + -6

Combine like terms: 10 + -6 = 4
x = 4

Simplifying
x = 4

Subproblem 2
x + 6 = -10

Simplifying
x + 6 = -10

Reorder the terms:
6 + x = -10

Solving
6 + x = -10

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -10 + -6

Combine like terms: 6 + -6 = 0
0 + x = -10 + -6
x = -10 + -6

Combine like terms: -10 + -6 = -16
x = -16

Simplifying
x = -16

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -16}