y^2-12y+36=2y^2+5y+42

Solution for y^2-12y+36=2y^2+5y+42 equation:

Simplifying
y2 + -12y + 36 = 2y2 + 5y + 42

Reorder the terms:
36 + -12y + y2 = 2y2 + 5y + 42

Reorder the terms:
36 + -12y + y2 = 42 + 5y + 2y2

Solving
36 + -12y + y2 = 42 + 5y + 2y2

Solving for variable 'y'.

Reorder the terms:
36 + -42 + -12y + -5y + y2 + -2y2 = 42 + 5y + 2y2 + -42 + -5y + -2y2

Combine like terms: 36 + -42 = -6
-6 + -12y + -5y + y2 + -2y2 = 42 + 5y + 2y2 + -42 + -5y + -2y2

Combine like terms: -12y + -5y = -17y
-6 + -17y + y2 + -2y2 = 42 + 5y + 2y2 + -42 + -5y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-6 + -17y + -1y2 = 42 + 5y + 2y2 + -42 + -5y + -2y2

Reorder the terms:
-6 + -17y + -1y2 = 42 + -42 + 5y + -5y + 2y2 + -2y2

Combine like terms: 42 + -42 = 0
-6 + -17y + -1y2 = 0 + 5y + -5y + 2y2 + -2y2
-6 + -17y + -1y2 = 5y + -5y + 2y2 + -2y2

Combine like terms: 5y + -5y = 0
-6 + -17y + -1y2 = 0 + 2y2 + -2y2
-6 + -17y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-6 + -17y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 17y + y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 17y + y2)' equal to zero and attempt to solve:

Simplifying
6 + 17y + y2 = 0

Solving
6 + 17y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 17y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + 17y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 17y + y2 = 0 + -6
17y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
17y + y2 = -6

The y term is 17y.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17y + 72.25 + y2 = -6 + 72.25

Reorder the terms:
72.25 + 17y + y2 = -6 + 72.25

Combine like terms: -6 + 72.25 = 66.25
72.25 + 17y + y2 = 66.25

Factor a perfect square on the left side:
(y + 8.5)(y + 8.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(y + 8.5) equal to 8.139410298 and -8.139410298.

Subproblem 1
y + 8.5 = 8.139410298

Simplifying
y + 8.5 = 8.139410298

Reorder the terms:
8.5 + y = 8.139410298

Solving
8.5 + y = 8.139410298

Solving for variable 'y'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + y = 8.139410298 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + y = 8.139410298 + -8.5
y = 8.139410298 + -8.5

Combine like terms: 8.139410298 + -8.5 = -0.360589702
y = -0.360589702

Simplifying
y = -0.360589702

Subproblem 2
y + 8.5 = -8.139410298

Simplifying
y + 8.5 = -8.139410298

Reorder the terms:
8.5 + y = -8.139410298

Solving
8.5 + y = -8.139410298

Solving for variable 'y'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + y = -8.139410298 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + y = -8.139410298 + -8.5
y = -8.139410298 + -8.5

Combine like terms: -8.139410298 + -8.5 = -16.639410298
y = -16.639410298

Simplifying
y = -16.639410298

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.360589702, -16.639410298}
Solution
y = {-0.360589702, -16.639410298}