6(x^2-x-12)=60

Solution for 6(x^2-x-12)=60 equation:

Simplifying
6(x2 + -1x + -12) = 60

Reorder the terms:
6(-12 + -1x + x2) = 60
(-12 * 6 + -1x * 6 + x2 * 6) = 60
(-72 + -6x + 6x2) = 60

Solving
-72 + -6x + 6x2 = 60

Solving for variable 'x'.

Reorder the terms:
-72 + -60 + -6x + 6x2 = 60 + -60

Combine like terms: -72 + -60 = -132
-132 + -6x + 6x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-132 + -6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-22 + -1x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-22 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-22 + -1x + x2 = 0

Solving
-22 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -1x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -1x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x + x2 = 0 + 22
-1x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-1x + x2 = 22

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.
-1x + 0.25 + x2 = 22 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + -1x + x2 = 22.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
x + -0.5 = 4.716990566

Simplifying
x + -0.5 = 4.716990566

Reorder the terms:
-0.5 + x = 4.716990566

Solving
-0.5 + x = 4.716990566

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 = 4.716990566 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.716990566 + 0.5
x = 4.716990566 + 0.5

Combine like terms: 4.716990566 + 0.5 = 5.216990566
x = 5.216990566

Simplifying
x = 5.216990566

Subproblem 2
x + -0.5 = -4.716990566

Simplifying
x + -0.5 = -4.716990566

Reorder the terms:
-0.5 + x = -4.716990566

Solving
-0.5 + x = -4.716990566

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 = -4.716990566 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.716990566 + 0.5
x = -4.716990566 + 0.5

Combine like terms: -4.716990566 + 0.5 = -4.216990566
x = -4.216990566

Simplifying
x = -4.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.216990566, -4.216990566}
Solution
x = {5.216990566, -4.216990566}