2(3y-25)(4y+2)=26

Solution for 2(3y-25)(4y+2)=26 equation:

Simplifying
2(3y + -25)(4y + 2) = 26

Reorder the terms:
2(-25 + 3y)(4y + 2) = 26

Reorder the terms:
2(-25 + 3y)(2 + 4y) = 26

Multiply (-25 + 3y) * (2 + 4y)
2(-25(2 + 4y) + 3y * (2 + 4y)) = 26
2((2 * -25 + 4y * -25) + 3y * (2 + 4y)) = 26
2((-50 + -100y) + 3y * (2 + 4y)) = 26
2(-50 + -100y + (2 * 3y + 4y * 3y)) = 26
2(-50 + -100y + (6y + 12y2)) = 26

Combine like terms: -100y + 6y = -94y
2(-50 + -94y + 12y2) = 26
(-50 * 2 + -94y * 2 + 12y2 * 2) = 26
(-100 + -188y + 24y2) = 26

Solving
-100 + -188y + 24y2 = 26

Solving for variable 'y'.

Reorder the terms:
-100 + -26 + -188y + 24y2 = 26 + -26

Combine like terms: -100 + -26 = -126
-126 + -188y + 24y2 = 26 + -26

Combine like terms: 26 + -26 = 0
-126 + -188y + 24y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + -94y + 12y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-63 + -94y + 12y2)' equal to zero and attempt to solve:

Simplifying
-63 + -94y + 12y2 = 0

Solving
-63 + -94y + 12y2 = 0

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

Divide each side by '12'.
-5.25 + -7.833333333y + y2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -7.833333333y + 5.25 + y2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -7.833333333y + y2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -7.833333333y + y2 = 0 + 5.25
-7.833333333y + y2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-7.833333333y + y2 = 5.25

The y term is -7.833333333y.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333y + 15.34027778 + y2 = 5.25 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333y + y2 = 5.25 + 15.34027778

Combine like terms: 5.25 + 15.34027778 = 20.59027778
15.34027778 + -7.833333333y + y2 = 20.59027778

Factor a perfect square on the left side:
(y + -3.916666667)(y + -3.916666667) = 20.59027778

Calculate the square root of the right side: 4.53765113

Break this problem into two subproblems by setting 
(y + -3.916666667) equal to 4.53765113 and -4.53765113.

Subproblem 1
y + -3.916666667 = 4.53765113

Simplifying
y + -3.916666667 = 4.53765113

Reorder the terms:
-3.916666667 + y = 4.53765113

Solving
-3.916666667 + y = 4.53765113

Solving for variable 'y'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + y = 4.53765113 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + y = 4.53765113 + 3.916666667
y = 4.53765113 + 3.916666667

Combine like terms: 4.53765113 + 3.916666667 = 8.454317797
y = 8.454317797

Simplifying
y = 8.454317797

Subproblem 2
y + -3.916666667 = -4.53765113

Simplifying
y + -3.916666667 = -4.53765113

Reorder the terms:
-3.916666667 + y = -4.53765113

Solving
-3.916666667 + y = -4.53765113

Solving for variable 'y'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + y = -4.53765113 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + y = -4.53765113 + 3.916666667
y = -4.53765113 + 3.916666667

Combine like terms: -4.53765113 + 3.916666667 = -0.620984463
y = -0.620984463

Simplifying
y = -0.620984463

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.454317797, -0.620984463}
Solution
y = {8.454317797, -0.620984463}