y^2-8y+16=2y^2-12y-5

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Solution for y^2-8y+16=2y^2-12y-5 equation: 


Simplifying
y2 + -8y + 16 = 2y2 + -12y + -5

Reorder the terms:
16 + -8y + y2 = 2y2 + -12y + -5

Reorder the terms:
16 + -8y + y2 = -5 + -12y + 2y2

Solving
16 + -8y + y2 = -5 + -12y + 2y2

Solving for variable 'y'.

Reorder the terms:
16 + 5 + -8y + 12y + y2 + -2y2 = -5 + -12y + 2y2 + 5 + 12y + -2y2

Combine like terms: 16 + 5 = 21
21 + -8y + 12y + y2 + -2y2 = -5 + -12y + 2y2 + 5 + 12y + -2y2

Combine like terms: -8y + 12y = 4y
21 + 4y + y2 + -2y2 = -5 + -12y + 2y2 + 5 + 12y + -2y2

Combine like terms: y2 + -2y2 = -1y2
21 + 4y + -1y2 = -5 + -12y + 2y2 + 5 + 12y + -2y2

Reorder the terms:
21 + 4y + -1y2 = -5 + 5 + -12y + 12y + 2y2 + -2y2

Combine like terms: -5 + 5 = 0
21 + 4y + -1y2 = 0 + -12y + 12y + 2y2 + -2y2
21 + 4y + -1y2 = -12y + 12y + 2y2 + -2y2

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

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

Factor a trinomial.
(7 + -1y)(3 + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

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

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