3(x+5)(x-5)-12=5(3x+3)+60

Solution for 3(x+5)(x-5)-12=5(3x+3)+60 equation:

Simplifying
3(x + 5)(x + -5) + -12 = 5(3x + 3) + 60

Reorder the terms:
3(5 + x)(x + -5) + -12 = 5(3x + 3) + 60

Reorder the terms:
3(5 + x)(-5 + x) + -12 = 5(3x + 3) + 60

Multiply (5 + x) * (-5 + x)
3(5(-5 + x) + x(-5 + x)) + -12 = 5(3x + 3) + 60
3((-5 * 5 + x * 5) + x(-5 + x)) + -12 = 5(3x + 3) + 60
3((-25 + 5x) + x(-5 + x)) + -12 = 5(3x + 3) + 60
3(-25 + 5x + (-5 * x + x * x)) + -12 = 5(3x + 3) + 60
3(-25 + 5x + (-5x + x2)) + -12 = 5(3x + 3) + 60

Combine like terms: 5x + -5x = 0
3(-25 + 0 + x2) + -12 = 5(3x + 3) + 60
3(-25 + x2) + -12 = 5(3x + 3) + 60
(-25 * 3 + x2 * 3) + -12 = 5(3x + 3) + 60
(-75 + 3x2) + -12 = 5(3x + 3) + 60

Reorder the terms:
-75 + -12 + 3x2 = 5(3x + 3) + 60

Combine like terms: -75 + -12 = -87
-87 + 3x2 = 5(3x + 3) + 60

Reorder the terms:
-87 + 3x2 = 5(3 + 3x) + 60
-87 + 3x2 = (3 * 5 + 3x * 5) + 60
-87 + 3x2 = (15 + 15x) + 60

Reorder the terms:
-87 + 3x2 = 15 + 60 + 15x

Combine like terms: 15 + 60 = 75
-87 + 3x2 = 75 + 15x

Solving
-87 + 3x2 = 75 + 15x

Solving for variable 'x'.

Reorder the terms:
-87 + -75 + -15x + 3x2 = 75 + 15x + -75 + -15x

Combine like terms: -87 + -75 = -162
-162 + -15x + 3x2 = 75 + 15x + -75 + -15x

Reorder the terms:
-162 + -15x + 3x2 = 75 + -75 + 15x + -15x

Combine like terms: 75 + -75 = 0
-162 + -15x + 3x2 = 0 + 15x + -15x
-162 + -15x + 3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-162 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-54 + -5x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-54 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-54 + -5x + x2 = 0

Solving
-54 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -5x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -5x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -5x + x2 = 0 + 54
-5x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-5x + x2 = 54

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 54 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 54 + 6.25

Combine like terms: 54 + 6.25 = 60.25
6.25 + -5x + x2 = 60.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.762087348 and -7.762087348.

Subproblem 1
x + -2.5 = 7.762087348

Simplifying
x + -2.5 = 7.762087348

Reorder the terms:
-2.5 + x = 7.762087348

Solving
-2.5 + x = 7.762087348

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.762087348 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.762087348 + 2.5
x = 7.762087348 + 2.5

Combine like terms: 7.762087348 + 2.5 = 10.262087348
x = 10.262087348

Simplifying
x = 10.262087348

Subproblem 2
x + -2.5 = -7.762087348

Simplifying
x + -2.5 = -7.762087348

Reorder the terms:
-2.5 + x = -7.762087348

Solving
-2.5 + x = -7.762087348

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.762087348 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.762087348 + 2.5
x = -7.762087348 + 2.5

Combine like terms: -7.762087348 + 2.5 = -5.262087348
x = -5.262087348

Simplifying
x = -5.262087348

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.262087348, -5.262087348}
Solution
x = {10.262087348, -5.262087348}