y^2-6y-12=0

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Solution for y^2-6y-12=0 equation: 


Simplifying
y2 + -6y + -12 = 0

Reorder the terms:
-12 + -6y + y2 = 0

Solving
-12 + -6y + 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 + -6y + 12 + y2 = 0 + 12

Reorder the terms:
-12 + 12 + -6y + y2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -6y + y2 = 0 + 12
-6y + y2 = 0 + 12

Combine like terms: 0 + 12 = 12
-6y + y2 = 12

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = 12 + 9

Reorder the terms:
9 + -6y + y2 = 12 + 9

Combine like terms: 12 + 9 = 21
9 + -6y + y2 = 21

Factor a perfect square on the left side:
(y + -3)(y + -3) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(y + -3) equal to 4.582575695 and -4.582575695.


Subproblem 1
y + -3 = 4.582575695

Simplifying
y + -3 = 4.582575695

Reorder the terms:
-3 + y = 4.582575695

Solving
-3 + y = 4.582575695

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = 4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + y = 4.582575695 + 3
y = 4.582575695 + 3

Combine like terms: 4.582575695 + 3 = 7.582575695
y = 7.582575695

Simplifying
y = 7.582575695


Subproblem 2
y + -3 = -4.582575695

Simplifying
y + -3 = -4.582575695

Reorder the terms:
-3 + y = -4.582575695

Solving
-3 + y = -4.582575695

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = -4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + y = -4.582575695 + 3
y = -4.582575695 + 3

Combine like terms: -4.582575695 + 3 = -1.582575695
y = -1.582575695

Simplifying
y = -1.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.582575695, -1.582575695}

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