(6x+4)(4x-10)=180

Solution for (6x+4)(4x-10)=180 equation:

Simplifying
(6x + 4)(4x + -10) = 180

Reorder the terms:
(4 + 6x)(4x + -10) = 180

Reorder the terms:
(4 + 6x)(-10 + 4x) = 180

Multiply (4 + 6x) * (-10 + 4x)
(4(-10 + 4x) + 6x * (-10 + 4x)) = 180
((-10 * 4 + 4x * 4) + 6x * (-10 + 4x)) = 180
((-40 + 16x) + 6x * (-10 + 4x)) = 180
(-40 + 16x + (-10 * 6x + 4x * 6x)) = 180
(-40 + 16x + (-60x + 24x2)) = 180

Combine like terms: 16x + -60x = -44x
(-40 + -44x + 24x2) = 180

Solving
-40 + -44x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
-40 + -180 + -44x + 24x2 = 180 + -180

Combine like terms: -40 + -180 = -220
-220 + -44x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-220 + -44x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-55 + -11x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-55 + -11x + 6x2)' equal to zero and attempt to solve:

Simplifying
-55 + -11x + 6x2 = 0

Solving
-55 + -11x + 6x2 = 0

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

Divide each side by '6'.
-9.166666667 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '9.166666667' to each side of the equation.
-9.166666667 + -1.833333333x + 9.166666667 + x2 = 0 + 9.166666667

Reorder the terms:
-9.166666667 + 9.166666667 + -1.833333333x + x2 = 0 + 9.166666667

Combine like terms: -9.166666667 + 9.166666667 = 0.000000000
0.000000000 + -1.833333333x + x2 = 0 + 9.166666667
-1.833333333x + x2 = 0 + 9.166666667

Combine like terms: 0 + 9.166666667 = 9.166666667
-1.833333333x + x2 = 9.166666667

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = 9.166666667 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 9.166666667 + 0.8402777775

Combine like terms: 9.166666667 + 0.8402777775 = 10.0069444445
0.8402777775 + -1.833333333x + x2 = 10.0069444445

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 10.0069444445

Calculate the square root of the right side: 3.163375483

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 3.163375483 and -3.163375483.

Subproblem 1
x + -0.9166666665 = 3.163375483

Simplifying
x + -0.9166666665 = 3.163375483

Reorder the terms:
-0.9166666665 + x = 3.163375483

Solving
-0.9166666665 + x = 3.163375483

Solving for variable 'x'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + x = 3.163375483 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = 3.163375483 + 0.9166666665
x = 3.163375483 + 0.9166666665

Combine like terms: 3.163375483 + 0.9166666665 = 4.0800421495
x = 4.0800421495

Simplifying
x = 4.0800421495

Subproblem 2
x + -0.9166666665 = -3.163375483

Simplifying
x + -0.9166666665 = -3.163375483

Reorder the terms:
-0.9166666665 + x = -3.163375483

Solving
-0.9166666665 + x = -3.163375483

Solving for variable 'x'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + x = -3.163375483 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = -3.163375483 + 0.9166666665
x = -3.163375483 + 0.9166666665

Combine like terms: -3.163375483 + 0.9166666665 = -2.2467088165
x = -2.2467088165

Simplifying
x = -2.2467088165

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.0800421495, -2.2467088165}
Solution
x = {4.0800421495, -2.2467088165}