2(x+5)*3(x-3)=26

Solution for 2(x+5)*3(x-3)=26 equation:

Simplifying
2(x + 5) * 3(x + -3) = 26

Reorder the terms:
2(5 + x) * 3(x + -3) = 26

Reorder the terms:
2(5 + x) * 3(-3 + x) = 26

Reorder the terms for easier multiplication:
2 * 3(5 + x)(-3 + x) = 26

Multiply 2 * 3
6(5 + x)(-3 + x) = 26

Multiply (5 + x) * (-3 + x)
6(5(-3 + x) + x(-3 + x)) = 26
6((-3 * 5 + x * 5) + x(-3 + x)) = 26
6((-15 + 5x) + x(-3 + x)) = 26
6(-15 + 5x + (-3 * x + x * x)) = 26
6(-15 + 5x + (-3x + x2)) = 26

Combine like terms: 5x + -3x = 2x
6(-15 + 2x + x2) = 26
(-15 * 6 + 2x * 6 + x2 * 6) = 26
(-90 + 12x + 6x2) = 26

Solving
-90 + 12x + 6x2 = 26

Solving for variable 'x'.

Reorder the terms:
-90 + -26 + 12x + 6x2 = 26 + -26

Combine like terms: -90 + -26 = -116
-116 + 12x + 6x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-116 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-58 + 6x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-58 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-58 + 6x + 3x2 = 0

Solving
-58 + 6x + 3x2 = 0

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

Divide each side by '3'.
-19.33333333 + 2x + x2 = 0

Move the constant term to the right:

Add '19.33333333' to each side of the equation.
-19.33333333 + 2x + 19.33333333 + x2 = 0 + 19.33333333

Reorder the terms:
-19.33333333 + 19.33333333 + 2x + x2 = 0 + 19.33333333

Combine like terms: -19.33333333 + 19.33333333 = 0.00000000
0.00000000 + 2x + x2 = 0 + 19.33333333
2x + x2 = 0 + 19.33333333

Combine like terms: 0 + 19.33333333 = 19.33333333
2x + x2 = 19.33333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 19.33333333 + 1

Reorder the terms:
1 + 2x + x2 = 19.33333333 + 1

Combine like terms: 19.33333333 + 1 = 20.33333333
1 + 2x + x2 = 20.33333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20.33333333

Calculate the square root of the right side: 4.509249752

Break this problem into two subproblems by setting 
(x + 1) equal to 4.509249752 and -4.509249752.

Subproblem 1
x + 1 = 4.509249752

Simplifying
x + 1 = 4.509249752

Reorder the terms:
1 + x = 4.509249752

Solving
1 + x = 4.509249752

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.509249752 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.509249752 + -1
x = 4.509249752 + -1

Combine like terms: 4.509249752 + -1 = 3.509249752
x = 3.509249752

Simplifying
x = 3.509249752

Subproblem 2
x + 1 = -4.509249752

Simplifying
x + 1 = -4.509249752

Reorder the terms:
1 + x = -4.509249752

Solving
1 + x = -4.509249752

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.509249752 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.509249752 + -1
x = -4.509249752 + -1

Combine like terms: -4.509249752 + -1 = -5.509249752
x = -5.509249752

Simplifying
x = -5.509249752

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.509249752, -5.509249752}
Solution
x = {3.509249752, -5.509249752}