10y^2-12y-10=0

Solution for 10y^2-12y-10=0 equation:

Simplifying
10y2 + -12y + -10 = 0

Reorder the terms:
-10 + -12y + 10y2 = 0

Solving
-10 + -12y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6y + 5y2)' equal to zero and attempt to solve:

Simplifying
-5 + -6y + 5y2 = 0

Solving
-5 + -6y + 5y2 = 0

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

Divide each side by '5'.
-1 + -1.2y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.2y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.2y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.2y + y2 = 0 + 1
-1.2y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.2y + y2 = 1

The y term is -1.2y.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2y + 0.36 + y2 = 1 + 0.36

Reorder the terms:
0.36 + -1.2y + y2 = 1 + 0.36

Combine like terms: 1 + 0.36 = 1.36
0.36 + -1.2y + y2 = 1.36

Factor a perfect square on the left side:
(y + -0.6)(y + -0.6) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(y + -0.6) equal to 1.166190379 and -1.166190379.

Subproblem 1
y + -0.6 = 1.166190379

Simplifying
y + -0.6 = 1.166190379

Reorder the terms:
-0.6 + y = 1.166190379

Solving
-0.6 + y = 1.166190379

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = 1.166190379 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = 1.166190379 + 0.6
y = 1.166190379 + 0.6

Combine like terms: 1.166190379 + 0.6 = 1.766190379
y = 1.766190379

Simplifying
y = 1.766190379

Subproblem 2
y + -0.6 = -1.166190379

Simplifying
y + -0.6 = -1.166190379

Reorder the terms:
-0.6 + y = -1.166190379

Solving
-0.6 + y = -1.166190379

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = -1.166190379 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = -1.166190379 + 0.6
y = -1.166190379 + 0.6

Combine like terms: -1.166190379 + 0.6 = -0.566190379
y = -0.566190379

Simplifying
y = -0.566190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.766190379, -0.566190379}
Solution
y = {1.766190379, -0.566190379}