(x+3)*(x-2)=120

Solution for (x+3)*(x-2)=120 equation:

Simplifying
(x + 3)(x + -2) = 120

Reorder the terms:
(3 + x)(x + -2) = 120

Reorder the terms:
(3 + x)(-2 + x) = 120

Multiply (3 + x) * (-2 + x)
(3(-2 + x) + x(-2 + x)) = 120
((-2 * 3 + x * 3) + x(-2 + x)) = 120
((-6 + 3x) + x(-2 + x)) = 120
(-6 + 3x + (-2 * x + x * x)) = 120
(-6 + 3x + (-2x + x2)) = 120

Combine like terms: 3x + -2x = 1x
(-6 + 1x + x2) = 120

Solving
-6 + 1x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
-6 + -120 + 1x + x2 = 120 + -120

Combine like terms: -6 + -120 = -126
-126 + 1x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-126 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + 1x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + 1x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + 1x + x2 = 0 + 126
1x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
1x + x2 = 126

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 = 126 + 0.25

Reorder the terms:
0.25 + x + x2 = 126 + 0.25

Combine like terms: 126 + 0.25 = 126.25
0.25 + x + x2 = 126.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.236102527 and -11.236102527.

Subproblem 1
x + 0.5 = 11.236102527

Simplifying
x + 0.5 = 11.236102527

Reorder the terms:
0.5 + x = 11.236102527

Solving
0.5 + x = 11.236102527

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 = 11.236102527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.236102527 + -0.5
x = 11.236102527 + -0.5

Combine like terms: 11.236102527 + -0.5 = 10.736102527
x = 10.736102527

Simplifying
x = 10.736102527

Subproblem 2
x + 0.5 = -11.236102527

Simplifying
x + 0.5 = -11.236102527

Reorder the terms:
0.5 + x = -11.236102527

Solving
0.5 + x = -11.236102527

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 = -11.236102527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.236102527 + -0.5
x = -11.236102527 + -0.5

Combine like terms: -11.236102527 + -0.5 = -11.736102527
x = -11.736102527

Simplifying
x = -11.736102527

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.736102527, -11.736102527}