y^2-12y-32=0

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Solution for y^2-12y-32=0 equation: 


Simplifying
y2 + -12y + -32 = 0

Reorder the terms:
-32 + -12y + y2 = 0

Solving
-32 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -12y + 32 + y2 = 0 + 32

Reorder the terms:
-32 + 32 + -12y + y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -12y + y2 = 0 + 32
-12y + y2 = 0 + 32

Combine like terms: 0 + 32 = 32
-12y + y2 = 32

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 32 + 36

Reorder the terms:
36 + -12y + y2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + -12y + y2 = 68

Factor a perfect square on the left side:
(y + -6)(y + -6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(y + -6) equal to 8.246211251 and -8.246211251.


Subproblem 1
y + -6 = 8.246211251

Simplifying
y + -6 = 8.246211251

Reorder the terms:
-6 + y = 8.246211251

Solving
-6 + y = 8.246211251

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 8.246211251 + 6

Combine like terms: -6 + 6 = 0
0 + y = 8.246211251 + 6
y = 8.246211251 + 6

Combine like terms: 8.246211251 + 6 = 14.246211251
y = 14.246211251

Simplifying
y = 14.246211251


Subproblem 2
y + -6 = -8.246211251

Simplifying
y + -6 = -8.246211251

Reorder the terms:
-6 + y = -8.246211251

Solving
-6 + y = -8.246211251

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -8.246211251 + 6

Combine like terms: -6 + 6 = 0
0 + y = -8.246211251 + 6
y = -8.246211251 + 6

Combine like terms: -8.246211251 + 6 = -2.246211251
y = -2.246211251

Simplifying
y = -2.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.246211251, -2.246211251}

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