12(x-11)(x-11)+12=30

Solution for 12(x-11)(x-11)+12=30 equation:

Simplifying
12(x + -11)(x + -11) + 12 = 30

Reorder the terms:
12(-11 + x)(x + -11) + 12 = 30

Reorder the terms:
12(-11 + x)(-11 + x) + 12 = 30

Multiply (-11 + x) * (-11 + x)
12(-11(-11 + x) + x(-11 + x)) + 12 = 30
12((-11 * -11 + x * -11) + x(-11 + x)) + 12 = 30
12((121 + -11x) + x(-11 + x)) + 12 = 30
12(121 + -11x + (-11 * x + x * x)) + 12 = 30
12(121 + -11x + (-11x + x2)) + 12 = 30

Combine like terms: -11x + -11x = -22x
12(121 + -22x + x2) + 12 = 30
(121 * 12 + -22x * 12 + x2 * 12) + 12 = 30
(1452 + -264x + 12x2) + 12 = 30

Reorder the terms:
1452 + 12 + -264x + 12x2 = 30

Combine like terms: 1452 + 12 = 1464
1464 + -264x + 12x2 = 30

Solving
1464 + -264x + 12x2 = 30

Solving for variable 'x'.

Reorder the terms:
1464 + -30 + -264x + 12x2 = 30 + -30

Combine like terms: 1464 + -30 = 1434
1434 + -264x + 12x2 = 30 + -30

Combine like terms: 30 + -30 = 0
1434 + -264x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(239 + -44x + 2x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(239 + -44x + 2x2)' equal to zero and attempt to solve:

Simplifying
239 + -44x + 2x2 = 0

Solving
239 + -44x + 2x2 = 0

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

Divide each side by '2'.
119.5 + -22x + x2 = 0

Move the constant term to the right:

Add '-119.5' to each side of the equation.
119.5 + -22x + -119.5 + x2 = 0 + -119.5

Reorder the terms:
119.5 + -119.5 + -22x + x2 = 0 + -119.5

Combine like terms: 119.5 + -119.5 = 0.0
0.0 + -22x + x2 = 0 + -119.5
-22x + x2 = 0 + -119.5

Combine like terms: 0 + -119.5 = -119.5
-22x + x2 = -119.5

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -119.5 + 121

Reorder the terms:
121 + -22x + x2 = -119.5 + 121

Combine like terms: -119.5 + 121 = 1.5
121 + -22x + x2 = 1.5

Factor a perfect square on the left side:
(x + -11)(x + -11) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -11) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + -11 = 1.224744871

Simplifying
x + -11 = 1.224744871

Reorder the terms:
-11 + x = 1.224744871

Solving
-11 + x = 1.224744871

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 1.224744871 + 11

Combine like terms: -11 + 11 = 0
0 + x = 1.224744871 + 11
x = 1.224744871 + 11

Combine like terms: 1.224744871 + 11 = 12.224744871
x = 12.224744871

Simplifying
x = 12.224744871

Subproblem 2
x + -11 = -1.224744871

Simplifying
x + -11 = -1.224744871

Reorder the terms:
-11 + x = -1.224744871

Solving
-11 + x = -1.224744871

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -1.224744871 + 11

Combine like terms: -11 + 11 = 0
0 + x = -1.224744871 + 11
x = -1.224744871 + 11

Combine like terms: -1.224744871 + 11 = 9.775255129
x = 9.775255129

Simplifying
x = 9.775255129

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.224744871, 9.775255129}
Solution
x = {12.224744871, 9.775255129}