3(x-2)(x+2)=15(x+2)+15(x-2)

Solution for 3(x-2)(x+2)=15(x+2)+15(x-2) equation:

Simplifying
3(x + -2)(x + 2) = 15(x + 2) + 15(x + -2)

Reorder the terms:
3(-2 + x)(x + 2) = 15(x + 2) + 15(x + -2)

Reorder the terms:
3(-2 + x)(2 + x) = 15(x + 2) + 15(x + -2)

Multiply (-2 + x) * (2 + x)
3(-2(2 + x) + x(2 + x)) = 15(x + 2) + 15(x + -2)
3((2 * -2 + x * -2) + x(2 + x)) = 15(x + 2) + 15(x + -2)
3((-4 + -2x) + x(2 + x)) = 15(x + 2) + 15(x + -2)
3(-4 + -2x + (2 * x + x * x)) = 15(x + 2) + 15(x + -2)
3(-4 + -2x + (2x + x2)) = 15(x + 2) + 15(x + -2)

Combine like terms: -2x + 2x = 0
3(-4 + 0 + x2) = 15(x + 2) + 15(x + -2)
3(-4 + x2) = 15(x + 2) + 15(x + -2)
(-4 * 3 + x2 * 3) = 15(x + 2) + 15(x + -2)
(-12 + 3x2) = 15(x + 2) + 15(x + -2)

Reorder the terms:
-12 + 3x2 = 15(2 + x) + 15(x + -2)
-12 + 3x2 = (2 * 15 + x * 15) + 15(x + -2)
-12 + 3x2 = (30 + 15x) + 15(x + -2)

Reorder the terms:
-12 + 3x2 = 30 + 15x + 15(-2 + x)
-12 + 3x2 = 30 + 15x + (-2 * 15 + x * 15)
-12 + 3x2 = 30 + 15x + (-30 + 15x)

Reorder the terms:
-12 + 3x2 = 30 + -30 + 15x + 15x

Combine like terms: 30 + -30 = 0
-12 + 3x2 = 0 + 15x + 15x
-12 + 3x2 = 15x + 15x

Combine like terms: 15x + 15x = 30x
-12 + 3x2 = 30x

Solving
-12 + 3x2 = 30x

Solving for variable 'x'.

Reorder the terms:
-12 + -30x + 3x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-12 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -10x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -10x + x2 = 0

Solving
-4 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -10x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -10x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -10x + x2 = 0 + 4
-10x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-10x + x2 = 4

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 4 + 25

Reorder the terms:
25 + -10x + x2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + -10x + x2 = 29

Factor a perfect square on the left side:
(x + -5)(x + -5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -5) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + -5 = 5.385164807

Simplifying
x + -5 = 5.385164807

Reorder the terms:
-5 + x = 5.385164807

Solving
-5 + x = 5.385164807

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.385164807 + 5
x = 5.385164807 + 5

Combine like terms: 5.385164807 + 5 = 10.385164807
x = 10.385164807

Simplifying
x = 10.385164807

Subproblem 2
x + -5 = -5.385164807

Simplifying
x + -5 = -5.385164807

Reorder the terms:
-5 + x = -5.385164807

Solving
-5 + x = -5.385164807

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.385164807 + 5
x = -5.385164807 + 5

Combine like terms: -5.385164807 + 5 = -0.385164807
x = -0.385164807

Simplifying
x = -0.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.385164807, -0.385164807}
Solution
x = {10.385164807, -0.385164807}