2y^2-8y+15-y^2+12y-36=0

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Solution for 2y^2-8y+15-y^2+12y-36=0 equation: 


Simplifying
2y2 + -8y + 15 + -1y2 + 12y + -36 = 0

Reorder the terms:
15 + -36 + -8y + 12y + 2y2 + -1y2 = 0

Combine like terms: 15 + -36 = -21
-21 + -8y + 12y + 2y2 + -1y2 = 0

Combine like terms: -8y + 12y = 4y
-21 + 4y + 2y2 + -1y2 = 0

Combine like terms: 2y2 + -1y2 = 1y2
-21 + 4y + 1y2 = 0

Solving
-21 + 4y + 1y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-7, 3}

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