0.5(x)(x+2)=12

Solution for 0.5(x)(x+2)=12 equation:

Simplifying
0.5(x)(x + 2) = 12

Reorder the terms:
0.5x(2 + x) = 12
(2 * 0.5x + x * 0.5x) = 12
(1x + 0.5x2) = 12

Solving
1x + 0.5x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 1x + 0.5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 1x + 0.5x2 = 0

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

Divide each side by '0.5'.
-24 + 2x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 2x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 2x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 2x + x2 = 0 + 24
2x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
2x + x2 = 24

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 24 + 1

Reorder the terms:
1 + 2x + x2 = 24 + 1

Combine like terms: 24 + 1 = 25
1 + 2x + x2 = 25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 1) equal to 5 and -5.

Subproblem 1
x + 1 = 5

Simplifying
x + 1 = 5

Reorder the terms:
1 + x = 5

Solving
1 + x = 5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5 + -1
x = 5 + -1

Combine like terms: 5 + -1 = 4
x = 4

Simplifying
x = 4

Subproblem 2
x + 1 = -5

Simplifying
x + 1 = -5

Reorder the terms:
1 + x = -5

Solving
1 + x = -5

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5 + -1
x = -5 + -1

Combine like terms: -5 + -1 = -6
x = -6

Simplifying
x = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -6}