7(8y^2-6y+4)-4(3y^2-5y+8)=

Solution for 7(8y^2-6y+4)-4(3y^2-5y+8)= equation:

Simplifying
7(8y2 + -6y + 4) + -4(3y2 + -5y + 8) = 0

Reorder the terms:
7(4 + -6y + 8y2) + -4(3y2 + -5y + 8) = 0
(4 * 7 + -6y * 7 + 8y2 * 7) + -4(3y2 + -5y + 8) = 0
(28 + -42y + 56y2) + -4(3y2 + -5y + 8) = 0

Reorder the terms:
28 + -42y + 56y2 + -4(8 + -5y + 3y2) = 0
28 + -42y + 56y2 + (8 * -4 + -5y * -4 + 3y2 * -4) = 0
28 + -42y + 56y2 + (-32 + 20y + -12y2) = 0

Reorder the terms:
28 + -32 + -42y + 20y + 56y2 + -12y2 = 0

Combine like terms: 28 + -32 = -4
-4 + -42y + 20y + 56y2 + -12y2 = 0

Combine like terms: -42y + 20y = -22y
-4 + -22y + 56y2 + -12y2 = 0

Combine like terms: 56y2 + -12y2 = 44y2
-4 + -22y + 44y2 = 0

Solving
-4 + -22y + 44y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -11y + 22y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -11y + 22y2)' equal to zero and attempt to solve:

Simplifying
-2 + -11y + 22y2 = 0

Solving
-2 + -11y + 22y2 = 0

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

Divide each side by '22'.
-0.09090909091 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + -0.5y + 0.09090909091 + y2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + -0.5y + y2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + -0.5y + y2 = 0 + 0.09090909091
-0.5y + y2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
-0.5y + y2 = 0.09090909091

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.09090909091 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.09090909091 + 0.0625

Combine like terms: 0.09090909091 + 0.0625 = 0.15340909091
0.0625 + -0.5y + y2 = 0.15340909091

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.15340909091

Calculate the square root of the right side: 0.391674726

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.391674726 and -0.391674726.

Subproblem 1
y + -0.25 = 0.391674726

Simplifying
y + -0.25 = 0.391674726

Reorder the terms:
-0.25 + y = 0.391674726

Solving
-0.25 + y = 0.391674726

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 0.391674726 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 0.391674726 + 0.25
y = 0.391674726 + 0.25

Combine like terms: 0.391674726 + 0.25 = 0.641674726
y = 0.641674726

Simplifying
y = 0.641674726

Subproblem 2
y + -0.25 = -0.391674726

Simplifying
y + -0.25 = -0.391674726

Reorder the terms:
-0.25 + y = -0.391674726

Solving
-0.25 + y = -0.391674726

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -0.391674726 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -0.391674726 + 0.25
y = -0.391674726 + 0.25

Combine like terms: -0.391674726 + 0.25 = -0.141674726
y = -0.141674726

Simplifying
y = -0.141674726

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.641674726, -0.141674726}
Solution
y = {0.641674726, -0.141674726}