(x+2)(x-3)=20

Solution for (x+2)(x-3)=20 equation:

Simplifying
(x + 2)(x + -3) = 20

Reorder the terms:
(2 + x)(x + -3) = 20

Reorder the terms:
(2 + x)(-3 + x) = 20

Multiply (2 + x) * (-3 + x)
(2(-3 + x) + x(-3 + x)) = 20
((-3 * 2 + x * 2) + x(-3 + x)) = 20
((-6 + 2x) + x(-3 + x)) = 20
(-6 + 2x + (-3 * x + x * x)) = 20
(-6 + 2x + (-3x + x2)) = 20

Combine like terms: 2x + -3x = -1x
(-6 + -1x + x2) = 20

Solving
-6 + -1x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-6 + -20 + -1x + x2 = 20 + -20

Combine like terms: -6 + -20 = -26
-26 + -1x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-26 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -1x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -1x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x + x2 = 0 + 26
-1x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-1x + x2 = 26

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 = 26 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 26 + 0.25

Combine like terms: 26 + 0.25 = 26.25
0.25 + -1x + x2 = 26.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
x + -0.5 = 5.123475383

Simplifying
x + -0.5 = 5.123475383

Reorder the terms:
-0.5 + x = 5.123475383

Solving
-0.5 + x = 5.123475383

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 = 5.123475383 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 5.123475383 + 0.5
x = 5.123475383 + 0.5

Combine like terms: 5.123475383 + 0.5 = 5.623475383
x = 5.623475383

Simplifying
x = 5.623475383

Subproblem 2
x + -0.5 = -5.123475383

Simplifying
x + -0.5 = -5.123475383

Reorder the terms:
-0.5 + x = -5.123475383

Solving
-0.5 + x = -5.123475383

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 = -5.123475383 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -5.123475383 + 0.5
x = -5.123475383 + 0.5

Combine like terms: -5.123475383 + 0.5 = -4.623475383
x = -4.623475383

Simplifying
x = -4.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.623475383, -4.623475383}