(6x+4)(4x-14)=180

Solution for (6x+4)(4x-14)=180 equation:

Simplifying
(6x + 4)(4x + -14) = 180

Reorder the terms:
(4 + 6x)(4x + -14) = 180

Reorder the terms:
(4 + 6x)(-14 + 4x) = 180

Multiply (4 + 6x) * (-14 + 4x)
(4(-14 + 4x) + 6x * (-14 + 4x)) = 180
((-14 * 4 + 4x * 4) + 6x * (-14 + 4x)) = 180
((-56 + 16x) + 6x * (-14 + 4x)) = 180
(-56 + 16x + (-14 * 6x + 4x * 6x)) = 180
(-56 + 16x + (-84x + 24x2)) = 180

Combine like terms: 16x + -84x = -68x
(-56 + -68x + 24x2) = 180

Solving
-56 + -68x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
-56 + -180 + -68x + 24x2 = 180 + -180

Combine like terms: -56 + -180 = -236
-236 + -68x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-236 + -68x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-59 + -17x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-59 + -17x + 6x2)' equal to zero and attempt to solve:

Simplifying
-59 + -17x + 6x2 = 0

Solving
-59 + -17x + 6x2 = 0

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

Divide each side by '6'.
-9.833333333 + -2.833333333x + x2 = 0

Move the constant term to the right:

Add '9.833333333' to each side of the equation.
-9.833333333 + -2.833333333x + 9.833333333 + x2 = 0 + 9.833333333

Reorder the terms:
-9.833333333 + 9.833333333 + -2.833333333x + x2 = 0 + 9.833333333

Combine like terms: -9.833333333 + 9.833333333 = 0.000000000
0.000000000 + -2.833333333x + x2 = 0 + 9.833333333
-2.833333333x + x2 = 0 + 9.833333333

Combine like terms: 0 + 9.833333333 = 9.833333333
-2.833333333x + x2 = 9.833333333

The x term is -2.833333333x.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333x + 2.006944445 + x2 = 9.833333333 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333x + x2 = 9.833333333 + 2.006944445

Combine like terms: 9.833333333 + 2.006944445 = 11.840277778
2.006944445 + -2.833333333x + x2 = 11.840277778

Factor a perfect square on the left side:
(x + -1.416666667)(x + -1.416666667) = 11.840277778

Calculate the square root of the right side: 3.44097047

Break this problem into two subproblems by setting 
(x + -1.416666667) equal to 3.44097047 and -3.44097047.

Subproblem 1
x + -1.416666667 = 3.44097047

Simplifying
x + -1.416666667 = 3.44097047

Reorder the terms:
-1.416666667 + x = 3.44097047

Solving
-1.416666667 + x = 3.44097047

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = 3.44097047 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = 3.44097047 + 1.416666667
x = 3.44097047 + 1.416666667

Combine like terms: 3.44097047 + 1.416666667 = 4.857637137
x = 4.857637137

Simplifying
x = 4.857637137

Subproblem 2
x + -1.416666667 = -3.44097047

Simplifying
x + -1.416666667 = -3.44097047

Reorder the terms:
-1.416666667 + x = -3.44097047

Solving
-1.416666667 + x = -3.44097047

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = -3.44097047 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = -3.44097047 + 1.416666667
x = -3.44097047 + 1.416666667

Combine like terms: -3.44097047 + 1.416666667 = -2.024303803
x = -2.024303803

Simplifying
x = -2.024303803

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.857637137, -2.024303803}
Solution
x = {4.857637137, -2.024303803}