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

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

Simplifying
8(2y2 + -7y + 4) + -7(2y2 + -2y + 6) = 0

Reorder the terms:
8(4 + -7y + 2y2) + -7(2y2 + -2y + 6) = 0
(4 * 8 + -7y * 8 + 2y2 * 8) + -7(2y2 + -2y + 6) = 0
(32 + -56y + 16y2) + -7(2y2 + -2y + 6) = 0

Reorder the terms:
32 + -56y + 16y2 + -7(6 + -2y + 2y2) = 0
32 + -56y + 16y2 + (6 * -7 + -2y * -7 + 2y2 * -7) = 0
32 + -56y + 16y2 + (-42 + 14y + -14y2) = 0

Reorder the terms:
32 + -42 + -56y + 14y + 16y2 + -14y2 = 0

Combine like terms: 32 + -42 = -10
-10 + -56y + 14y + 16y2 + -14y2 = 0

Combine like terms: -56y + 14y = -42y
-10 + -42y + 16y2 + -14y2 = 0

Combine like terms: 16y2 + -14y2 = 2y2
-10 + -42y + 2y2 = 0

Solving
-10 + -42y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -21y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -21y + y2)' equal to zero and attempt to solve:

Simplifying
-5 + -21y + y2 = 0

Solving
-5 + -21y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -21y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -21y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -21y + y2 = 0 + 5
-21y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-21y + y2 = 5

The y term is -21y.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21y + 110.25 + y2 = 5 + 110.25

Reorder the terms:
110.25 + -21y + y2 = 5 + 110.25

Combine like terms: 5 + 110.25 = 115.25
110.25 + -21y + y2 = 115.25

Factor a perfect square on the left side:
(y + -10.5)(y + -10.5) = 115.25

Calculate the square root of the right side: 10.735455277

Break this problem into two subproblems by setting 
(y + -10.5) equal to 10.735455277 and -10.735455277.

Subproblem 1
y + -10.5 = 10.735455277

Simplifying
y + -10.5 = 10.735455277

Reorder the terms:
-10.5 + y = 10.735455277

Solving
-10.5 + y = 10.735455277

Solving for variable 'y'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + y = 10.735455277 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + y = 10.735455277 + 10.5
y = 10.735455277 + 10.5

Combine like terms: 10.735455277 + 10.5 = 21.235455277
y = 21.235455277

Simplifying
y = 21.235455277

Subproblem 2
y + -10.5 = -10.735455277

Simplifying
y + -10.5 = -10.735455277

Reorder the terms:
-10.5 + y = -10.735455277

Solving
-10.5 + y = -10.735455277

Solving for variable 'y'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + y = -10.735455277 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + y = -10.735455277 + 10.5
y = -10.735455277 + 10.5

Combine like terms: -10.735455277 + 10.5 = -0.235455277
y = -0.235455277

Simplifying
y = -0.235455277

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {21.235455277, -0.235455277}
Solution
y = {21.235455277, -0.235455277}