0=2y^2-20y+51-y^2+12y-36

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Solution for 0=2y^2-20y+51-y^2+12y-36 equation: 


Simplifying
0 = 2y2 + -20y + 51 + -1y2 + 12y + -36

Reorder the terms:
0 = 51 + -36 + -20y + 12y + 2y2 + -1y2

Combine like terms: 51 + -36 = 15
0 = 15 + -20y + 12y + 2y2 + -1y2

Combine like terms: -20y + 12y = -8y
0 = 15 + -8y + 2y2 + -1y2

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

Solving
0 = 15 + -8y + 1y2

Solving for variable 'y'.

Combine like terms: 0 + -15 = -15
-15 + 8y + -1y2 = 15 + -8y + 1y2 + -15 + 8y + -1y2

Reorder the terms:
-15 + 8y + -1y2 = 15 + -15 + -8y + 8y + 1y2 + -1y2

Combine like terms: 15 + -15 = 0
-15 + 8y + -1y2 = 0 + -8y + 8y + 1y2 + -1y2
-15 + 8y + -1y2 = -8y + 8y + 1y2 + -1y2

Combine like terms: -8y + 8y = 0
-15 + 8y + -1y2 = 0 + 1y2 + -1y2
-15 + 8y + -1y2 = 1y2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
-15 + 8y + -1y2 = 0

Factor a trinomial.
(-5 + y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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 = 0 + 5

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

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

Simplifying
y = 5

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 = {5, 3}

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