y^2-10y-12=0

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

Simplifying
y2 + -10y + -12 = 0

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

Solving
-12 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -10y + 12 + y2 = 0 + 12

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

Combine like terms: -12 + 12 = 0
0 + -10y + y2 = 0 + 12
-10y + y2 = 0 + 12

Combine like terms: 0 + 12 = 12
-10y + y2 = 12

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 12 + 25

Reorder the terms:
25 + -10y + y2 = 12 + 25

Combine like terms: 12 + 25 = 37
25 + -10y + y2 = 37

Factor a perfect square on the left side:
(y + -5)(y + -5) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(y + -5) equal to 6.08276253 and -6.08276253.

Subproblem 1
y + -5 = 6.08276253

Simplifying
y + -5 = 6.08276253

Reorder the terms:
-5 + y = 6.08276253

Solving
-5 + y = 6.08276253

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 6.08276253 + 5

Combine like terms: -5 + 5 = 0
0 + y = 6.08276253 + 5
y = 6.08276253 + 5

Combine like terms: 6.08276253 + 5 = 11.08276253
y = 11.08276253

Simplifying
y = 11.08276253

Subproblem 2
y + -5 = -6.08276253

Simplifying
y + -5 = -6.08276253

Reorder the terms:
-5 + y = -6.08276253

Solving
-5 + y = -6.08276253

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -6.08276253 + 5

Combine like terms: -5 + 5 = 0
0 + y = -6.08276253 + 5
y = -6.08276253 + 5

Combine like terms: -6.08276253 + 5 = -1.08276253
y = -1.08276253

Simplifying
y = -1.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.08276253, -1.08276253}