5(x+3)(x-6)-2(x-2)(x+5)=0

Solution for 5(x+3)(x-6)-2(x-2)(x+5)=0 equation:

Simplifying
5(x + 3)(x + -6) + -2(x + -2)(x + 5) = 0

Reorder the terms:
5(3 + x)(x + -6) + -2(x + -2)(x + 5) = 0

Reorder the terms:
5(3 + x)(-6 + x) + -2(x + -2)(x + 5) = 0

Multiply (3 + x) * (-6 + x)
5(3(-6 + x) + x(-6 + x)) + -2(x + -2)(x + 5) = 0
5((-6 * 3 + x * 3) + x(-6 + x)) + -2(x + -2)(x + 5) = 0
5((-18 + 3x) + x(-6 + x)) + -2(x + -2)(x + 5) = 0
5(-18 + 3x + (-6 * x + x * x)) + -2(x + -2)(x + 5) = 0
5(-18 + 3x + (-6x + x2)) + -2(x + -2)(x + 5) = 0

Combine like terms: 3x + -6x = -3x
5(-18 + -3x + x2) + -2(x + -2)(x + 5) = 0
(-18 * 5 + -3x * 5 + x2 * 5) + -2(x + -2)(x + 5) = 0
(-90 + -15x + 5x2) + -2(x + -2)(x + 5) = 0

Reorder the terms:
-90 + -15x + 5x2 + -2(-2 + x)(x + 5) = 0

Reorder the terms:
-90 + -15x + 5x2 + -2(-2 + x)(5 + x) = 0

Multiply (-2 + x) * (5 + x)
-90 + -15x + 5x2 + -2(-2(5 + x) + x(5 + x)) = 0
-90 + -15x + 5x2 + -2((5 * -2 + x * -2) + x(5 + x)) = 0
-90 + -15x + 5x2 + -2((-10 + -2x) + x(5 + x)) = 0
-90 + -15x + 5x2 + -2(-10 + -2x + (5 * x + x * x)) = 0
-90 + -15x + 5x2 + -2(-10 + -2x + (5x + x2)) = 0

Combine like terms: -2x + 5x = 3x
-90 + -15x + 5x2 + -2(-10 + 3x + x2) = 0
-90 + -15x + 5x2 + (-10 * -2 + 3x * -2 + x2 * -2) = 0
-90 + -15x + 5x2 + (20 + -6x + -2x2) = 0

Reorder the terms:
-90 + 20 + -15x + -6x + 5x2 + -2x2 = 0

Combine like terms: -90 + 20 = -70
-70 + -15x + -6x + 5x2 + -2x2 = 0

Combine like terms: -15x + -6x = -21x
-70 + -21x + 5x2 + -2x2 = 0

Combine like terms: 5x2 + -2x2 = 3x2
-70 + -21x + 3x2 = 0

Solving
-70 + -21x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-23.33333333 + -7x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + -7x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + -7x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + -7x + x2 = 0 + 23.33333333
-7x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
-7x + x2 = 23.33333333

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 23.33333333 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 23.33333333 + 12.25

Combine like terms: 23.33333333 + 12.25 = 35.58333333
12.25 + -7x + x2 = 35.58333333

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 35.58333333

Calculate the square root of the right side: 5.965176722

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.965176722 and -5.965176722.

Subproblem 1
x + -3.5 = 5.965176722

Simplifying
x + -3.5 = 5.965176722

Reorder the terms:
-3.5 + x = 5.965176722

Solving
-3.5 + x = 5.965176722

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 5.965176722 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 5.965176722 + 3.5
x = 5.965176722 + 3.5

Combine like terms: 5.965176722 + 3.5 = 9.465176722
x = 9.465176722

Simplifying
x = 9.465176722

Subproblem 2
x + -3.5 = -5.965176722

Simplifying
x + -3.5 = -5.965176722

Reorder the terms:
-3.5 + x = -5.965176722

Solving
-3.5 + x = -5.965176722

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -5.965176722 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -5.965176722 + 3.5
x = -5.965176722 + 3.5

Combine like terms: -5.965176722 + 3.5 = -2.465176722
x = -2.465176722

Simplifying
x = -2.465176722

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.465176722, -2.465176722}