(17x-6)(12x+12)=32

Solution for (17x-6)(12x+12)=32 equation:

Simplifying
(17x + -6)(12x + 12) = 32

Reorder the terms:
(-6 + 17x)(12x + 12) = 32

Reorder the terms:
(-6 + 17x)(12 + 12x) = 32

Multiply (-6 + 17x) * (12 + 12x)
(-6(12 + 12x) + 17x * (12 + 12x)) = 32
((12 * -6 + 12x * -6) + 17x * (12 + 12x)) = 32
((-72 + -72x) + 17x * (12 + 12x)) = 32
(-72 + -72x + (12 * 17x + 12x * 17x)) = 32
(-72 + -72x + (204x + 204x2)) = 32

Combine like terms: -72x + 204x = 132x
(-72 + 132x + 204x2) = 32

Solving
-72 + 132x + 204x2 = 32

Solving for variable 'x'.

Reorder the terms:
-72 + -32 + 132x + 204x2 = 32 + -32

Combine like terms: -72 + -32 = -104
-104 + 132x + 204x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-104 + 132x + 204x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-26 + 33x + 51x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-26 + 33x + 51x2)' equal to zero and attempt to solve:

Simplifying
-26 + 33x + 51x2 = 0

Solving
-26 + 33x + 51x2 = 0

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

Divide each side by '51'.
-0.5098039216 + 0.6470588235x + x2 = 0

Move the constant term to the right:

Add '0.5098039216' to each side of the equation.
-0.5098039216 + 0.6470588235x + 0.5098039216 + x2 = 0 + 0.5098039216

Reorder the terms:
-0.5098039216 + 0.5098039216 + 0.6470588235x + x2 = 0 + 0.5098039216

Combine like terms: -0.5098039216 + 0.5098039216 = 0.0000000000
0.0000000000 + 0.6470588235x + x2 = 0 + 0.5098039216
0.6470588235x + x2 = 0 + 0.5098039216

Combine like terms: 0 + 0.5098039216 = 0.5098039216
0.6470588235x + x2 = 0.5098039216

The x term is 0.6470588235x.  Take half its coefficient (0.3235294118).
Square it (0.1046712803) and add it to both sides.

Add '0.1046712803' to each side of the equation.
0.6470588235x + 0.1046712803 + x2 = 0.5098039216 + 0.1046712803

Reorder the terms:
0.1046712803 + 0.6470588235x + x2 = 0.5098039216 + 0.1046712803

Combine like terms: 0.5098039216 + 0.1046712803 = 0.6144752019
0.1046712803 + 0.6470588235x + x2 = 0.6144752019

Factor a perfect square on the left side:
(x + 0.3235294118)(x + 0.3235294118) = 0.6144752019

Calculate the square root of the right side: 0.783884687

Break this problem into two subproblems by setting 
(x + 0.3235294118) equal to 0.783884687 and -0.783884687.

Subproblem 1
x + 0.3235294118 = 0.783884687

Simplifying
x + 0.3235294118 = 0.783884687

Reorder the terms:
0.3235294118 + x = 0.783884687

Solving
0.3235294118 + x = 0.783884687

Solving for variable 'x'.

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

Add '-0.3235294118' to each side of the equation.
0.3235294118 + -0.3235294118 + x = 0.783884687 + -0.3235294118

Combine like terms: 0.3235294118 + -0.3235294118 = 0.0000000000
0.0000000000 + x = 0.783884687 + -0.3235294118
x = 0.783884687 + -0.3235294118

Combine like terms: 0.783884687 + -0.3235294118 = 0.4603552752
x = 0.4603552752

Simplifying
x = 0.4603552752

Subproblem 2
x + 0.3235294118 = -0.783884687

Simplifying
x + 0.3235294118 = -0.783884687

Reorder the terms:
0.3235294118 + x = -0.783884687

Solving
0.3235294118 + x = -0.783884687

Solving for variable 'x'.

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

Add '-0.3235294118' to each side of the equation.
0.3235294118 + -0.3235294118 + x = -0.783884687 + -0.3235294118

Combine like terms: 0.3235294118 + -0.3235294118 = 0.0000000000
0.0000000000 + x = -0.783884687 + -0.3235294118
x = -0.783884687 + -0.3235294118

Combine like terms: -0.783884687 + -0.3235294118 = -1.1074140988
x = -1.1074140988

Simplifying
x = -1.1074140988

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4603552752, -1.1074140988}
Solution
x = {0.4603552752, -1.1074140988}