(4x-2)(3x-5)=80

Solution for (4x-2)(3x-5)=80 equation:

Simplifying
(4x + -2)(3x + -5) = 80

Reorder the terms:
(-2 + 4x)(3x + -5) = 80

Reorder the terms:
(-2 + 4x)(-5 + 3x) = 80

Multiply (-2 + 4x) * (-5 + 3x)
(-2(-5 + 3x) + 4x * (-5 + 3x)) = 80
((-5 * -2 + 3x * -2) + 4x * (-5 + 3x)) = 80
((10 + -6x) + 4x * (-5 + 3x)) = 80
(10 + -6x + (-5 * 4x + 3x * 4x)) = 80
(10 + -6x + (-20x + 12x2)) = 80

Combine like terms: -6x + -20x = -26x
(10 + -26x + 12x2) = 80

Solving
10 + -26x + 12x2 = 80

Solving for variable 'x'.

Reorder the terms:
10 + -80 + -26x + 12x2 = 80 + -80

Combine like terms: 10 + -80 = -70
-70 + -26x + 12x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-70 + -26x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -13x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -13x + 6x2)' equal to zero and attempt to solve:

Simplifying
-35 + -13x + 6x2 = 0

Solving
-35 + -13x + 6x2 = 0

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

Divide each side by '6'.
-5.833333333 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -2.166666667x + 5.833333333 + x2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -2.166666667x + x2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -2.166666667x + x2 = 0 + 5.833333333
-2.166666667x + x2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-2.166666667x + x2 = 5.833333333

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = 5.833333333 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = 5.833333333 + 1.173611113

Combine like terms: 5.833333333 + 1.173611113 = 7.006944446
1.173611113 + -2.166666667x + x2 = 7.006944446

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 7.006944446

Calculate the square root of the right side: 2.647063363

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 2.647063363 and -2.647063363.

Subproblem 1
x + -1.083333334 = 2.647063363

Simplifying
x + -1.083333334 = 2.647063363

Reorder the terms:
-1.083333334 + x = 2.647063363

Solving
-1.083333334 + x = 2.647063363

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = 2.647063363 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = 2.647063363 + 1.083333334
x = 2.647063363 + 1.083333334

Combine like terms: 2.647063363 + 1.083333334 = 3.730396697
x = 3.730396697

Simplifying
x = 3.730396697

Subproblem 2
x + -1.083333334 = -2.647063363

Simplifying
x + -1.083333334 = -2.647063363

Reorder the terms:
-1.083333334 + x = -2.647063363

Solving
-1.083333334 + x = -2.647063363

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = -2.647063363 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = -2.647063363 + 1.083333334
x = -2.647063363 + 1.083333334

Combine like terms: -2.647063363 + 1.083333334 = -1.563730029
x = -1.563730029

Simplifying
x = -1.563730029

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.730396697, -1.563730029}
Solution
x = {3.730396697, -1.563730029}