(x-2)(x+3)=16

Solution for (x-2)(x+3)=16 equation:

Simplifying
(x + -2)(x + 3) = 16

Reorder the terms:
(-2 + x)(x + 3) = 16

Reorder the terms:
(-2 + x)(3 + x) = 16

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = 16
((3 * -2 + x * -2) + x(3 + x)) = 16
((-6 + -2x) + x(3 + x)) = 16
(-6 + -2x + (3 * x + x * x)) = 16
(-6 + -2x + (3x + x2)) = 16

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = 16

Solving
-6 + 1x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
-6 + -16 + 1x + x2 = 16 + -16

Combine like terms: -6 + -16 = -22
-22 + 1x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-22 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 1x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 1x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 1x + x2 = 0 + 22
1x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
1x + x2 = 22

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.
x + 0.25 + x2 = 22 + 0.25

Reorder the terms:
0.25 + x + x2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + x + x2 = 22.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + 0.5 = 4.716990566

Simplifying
x + 0.5 = 4.716990566

Reorder the terms:
0.5 + x = 4.716990566

Solving
0.5 + x = 4.716990566

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 = 4.716990566 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.716990566 + -0.5
x = 4.716990566 + -0.5

Combine like terms: 4.716990566 + -0.5 = 4.216990566
x = 4.216990566

Simplifying
x = 4.216990566

Subproblem 2
x + 0.5 = -4.716990566

Simplifying
x + 0.5 = -4.716990566

Reorder the terms:
0.5 + x = -4.716990566

Solving
0.5 + x = -4.716990566

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 = -4.716990566 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.716990566 + -0.5
x = -4.716990566 + -0.5

Combine like terms: -4.716990566 + -0.5 = -5.216990566
x = -5.216990566

Simplifying
x = -5.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.216990566, -5.216990566}