-10y^2-4(5y^2-8)+6y=

Solution for -10y^2-4(5y^2-8)+6y= equation:

Simplifying
-10y2 + -4(5y2 + -8) + 6y = 0

Reorder the terms:
-10y2 + -4(-8 + 5y2) + 6y = 0
-10y2 + (-8 * -4 + 5y2 * -4) + 6y = 0
-10y2 + (32 + -20y2) + 6y = 0

Reorder the terms:
32 + 6y + -10y2 + -20y2 = 0

Combine like terms: -10y2 + -20y2 = -30y2
32 + 6y + -30y2 = 0

Solving
32 + 6y + -30y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 3y + -15y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + 3y + -15y2)' equal to zero and attempt to solve:

Simplifying
16 + 3y + -15y2 = 0

Solving
16 + 3y + -15y2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1.066666667 + -0.2y + y2 = 0

Move the constant term to the right:

Add '1.066666667' to each side of the equation.
-1.066666667 + -0.2y + 1.066666667 + y2 = 0 + 1.066666667

Reorder the terms:
-1.066666667 + 1.066666667 + -0.2y + y2 = 0 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + -0.2y + y2 = 0 + 1.066666667
-0.2y + y2 = 0 + 1.066666667

Combine like terms: 0 + 1.066666667 = 1.066666667
-0.2y + y2 = 1.066666667

The y term is -0.2y.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2y + 0.01 + y2 = 1.066666667 + 0.01

Reorder the terms:
0.01 + -0.2y + y2 = 1.066666667 + 0.01

Combine like terms: 1.066666667 + 0.01 = 1.076666667
0.01 + -0.2y + y2 = 1.076666667

Factor a perfect square on the left side:
(y + -0.1)(y + -0.1) = 1.076666667

Calculate the square root of the right side: 1.037625495

Break this problem into two subproblems by setting 
(y + -0.1) equal to 1.037625495 and -1.037625495.

Subproblem 1
y + -0.1 = 1.037625495

Simplifying
y + -0.1 = 1.037625495

Reorder the terms:
-0.1 + y = 1.037625495

Solving
-0.1 + y = 1.037625495

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = 1.037625495 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = 1.037625495 + 0.1
y = 1.037625495 + 0.1

Combine like terms: 1.037625495 + 0.1 = 1.137625495
y = 1.137625495

Simplifying
y = 1.137625495

Subproblem 2
y + -0.1 = -1.037625495

Simplifying
y + -0.1 = -1.037625495

Reorder the terms:
-0.1 + y = -1.037625495

Solving
-0.1 + y = -1.037625495

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = -1.037625495 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = -1.037625495 + 0.1
y = -1.037625495 + 0.1

Combine like terms: -1.037625495 + 0.1 = -0.937625495
y = -0.937625495

Simplifying
y = -0.937625495

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.137625495, -0.937625495}
Solution
y = {1.137625495, -0.937625495}