0.5(x+2)(x-3)=63

Solution for 0.5(x+2)(x-3)=63 equation:

Simplifying
0.5(x + 2)(x + -3) = 63

Reorder the terms:
0.5(2 + x)(x + -3) = 63

Reorder the terms:
0.5(2 + x)(-3 + x) = 63

Multiply (2 + x) * (-3 + x)
0.5(2(-3 + x) + x(-3 + x)) = 63
0.5((-3 * 2 + x * 2) + x(-3 + x)) = 63
0.5((-6 + 2x) + x(-3 + x)) = 63
0.5(-6 + 2x + (-3 * x + x * x)) = 63
0.5(-6 + 2x + (-3x + x2)) = 63

Combine like terms: 2x + -3x = -1x
0.5(-6 + -1x + x2) = 63
(-6 * 0.5 + -1x * 0.5 + x2 * 0.5) = 63
(-3 + -0.5x + 0.5x2) = 63

Solving
-3 + -0.5x + 0.5x2 = 63

Solving for variable 'x'.

Reorder the terms:
-3 + -63 + -0.5x + 0.5x2 = 63 + -63

Combine like terms: -3 + -63 = -66
-66 + -0.5x + 0.5x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-66 + -0.5x + 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'.
-132 + -1x + x2 = 0

Move the constant term to the right:

Add '132' to each side of the equation.
-132 + -1x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + -1x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + -1x + x2 = 0 + 132
-1x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
-1x + x2 = 132

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 132 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 132 + 0.25

Combine like terms: 132 + 0.25 = 132.25
0.25 + -1x + x2 = 132.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 132.25

Calculate the square root of the right side: 11.5

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.5 and -11.5.

Subproblem 1
x + -0.5 = 11.5

Simplifying
x + -0.5 = 11.5

Reorder the terms:
-0.5 + x = 11.5

Solving
-0.5 + x = 11.5

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 11.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 11.5 + 0.5
x = 11.5 + 0.5

Combine like terms: 11.5 + 0.5 = 12
x = 12

Simplifying
x = 12

Subproblem 2
x + -0.5 = -11.5

Simplifying
x + -0.5 = -11.5

Reorder the terms:
-0.5 + x = -11.5

Solving
-0.5 + x = -11.5

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -11.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -11.5 + 0.5
x = -11.5 + 0.5

Combine like terms: -11.5 + 0.5 = -11
x = -11

Simplifying
x = -11

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, -11}