(7y+6)(5y-4)=128

Solution for (7y+6)(5y-4)=128 equation:

Simplifying
(7y + 6)(5y + -4) = 128

Reorder the terms:
(6 + 7y)(5y + -4) = 128

Reorder the terms:
(6 + 7y)(-4 + 5y) = 128

Multiply (6 + 7y) * (-4 + 5y)
(6(-4 + 5y) + 7y * (-4 + 5y)) = 128
((-4 * 6 + 5y * 6) + 7y * (-4 + 5y)) = 128
((-24 + 30y) + 7y * (-4 + 5y)) = 128
(-24 + 30y + (-4 * 7y + 5y * 7y)) = 128
(-24 + 30y + (-28y + 35y2)) = 128

Combine like terms: 30y + -28y = 2y
(-24 + 2y + 35y2) = 128

Solving
-24 + 2y + 35y2 = 128

Solving for variable 'y'.

Reorder the terms:
-24 + -128 + 2y + 35y2 = 128 + -128

Combine like terms: -24 + -128 = -152
-152 + 2y + 35y2 = 128 + -128

Combine like terms: 128 + -128 = 0
-152 + 2y + 35y2 = 0

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

Divide each side by '35'.
-4.342857143 + 0.05714285714y + y2 = 0

Move the constant term to the right:

Add '4.342857143' to each side of the equation.
-4.342857143 + 0.05714285714y + 4.342857143 + y2 = 0 + 4.342857143

Reorder the terms:
-4.342857143 + 4.342857143 + 0.05714285714y + y2 = 0 + 4.342857143

Combine like terms: -4.342857143 + 4.342857143 = 0.000000000
0.000000000 + 0.05714285714y + y2 = 0 + 4.342857143
0.05714285714y + y2 = 0 + 4.342857143

Combine like terms: 0 + 4.342857143 = 4.342857143
0.05714285714y + y2 = 4.342857143

The y term is 0.05714285714y.  Take half its coefficient (0.02857142857).
Square it (0.0008163265305) and add it to both sides.

Add '0.0008163265305' to each side of the equation.
0.05714285714y + 0.0008163265305 + y2 = 4.342857143 + 0.0008163265305

Reorder the terms:
0.0008163265305 + 0.05714285714y + y2 = 4.342857143 + 0.0008163265305

Combine like terms: 4.342857143 + 0.0008163265305 = 4.3436734695305
0.0008163265305 + 0.05714285714y + y2 = 4.3436734695305

Factor a perfect square on the left side:
(y + 0.02857142857)(y + 0.02857142857) = 4.3436734695305

Calculate the square root of the right side: 2.08414814

Break this problem into two subproblems by setting 
(y + 0.02857142857) equal to 2.08414814 and -2.08414814.

Subproblem 1
y + 0.02857142857 = 2.08414814

Simplifying
y + 0.02857142857 = 2.08414814

Reorder the terms:
0.02857142857 + y = 2.08414814

Solving
0.02857142857 + y = 2.08414814

Solving for variable 'y'.

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

Add '-0.02857142857' to each side of the equation.
0.02857142857 + -0.02857142857 + y = 2.08414814 + -0.02857142857

Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000
0.00000000000 + y = 2.08414814 + -0.02857142857
y = 2.08414814 + -0.02857142857

Combine like terms: 2.08414814 + -0.02857142857 = 2.05557671143
y = 2.05557671143

Simplifying
y = 2.05557671143

Subproblem 2
y + 0.02857142857 = -2.08414814

Simplifying
y + 0.02857142857 = -2.08414814

Reorder the terms:
0.02857142857 + y = -2.08414814

Solving
0.02857142857 + y = -2.08414814

Solving for variable 'y'.

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

Add '-0.02857142857' to each side of the equation.
0.02857142857 + -0.02857142857 + y = -2.08414814 + -0.02857142857

Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000
0.00000000000 + y = -2.08414814 + -0.02857142857
y = -2.08414814 + -0.02857142857

Combine like terms: -2.08414814 + -0.02857142857 = -2.11271956857
y = -2.11271956857

Simplifying
y = -2.11271956857

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.05557671143, -2.11271956857}