y^2-12y+36=2y^2-14y+28

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Solution for y^2-12y+36=2y^2-14y+28 equation: 


Simplifying
y2 + -12y + 36 = 2y2 + -14y + 28

Reorder the terms:
36 + -12y + y2 = 2y2 + -14y + 28

Reorder the terms:
36 + -12y + y2 = 28 + -14y + 2y2

Solving
36 + -12y + y2 = 28 + -14y + 2y2

Solving for variable 'y'.

Reorder the terms:
36 + -28 + -12y + 14y + y2 + -2y2 = 28 + -14y + 2y2 + -28 + 14y + -2y2

Combine like terms: 36 + -28 = 8
8 + -12y + 14y + y2 + -2y2 = 28 + -14y + 2y2 + -28 + 14y + -2y2

Combine like terms: -12y + 14y = 2y
8 + 2y + y2 + -2y2 = 28 + -14y + 2y2 + -28 + 14y + -2y2

Combine like terms: y2 + -2y2 = -1y2
8 + 2y + -1y2 = 28 + -14y + 2y2 + -28 + 14y + -2y2

Reorder the terms:
8 + 2y + -1y2 = 28 + -28 + -14y + 14y + 2y2 + -2y2

Combine like terms: 28 + -28 = 0
8 + 2y + -1y2 = 0 + -14y + 14y + 2y2 + -2y2
8 + 2y + -1y2 = -14y + 14y + 2y2 + -2y2

Combine like terms: -14y + 14y = 0
8 + 2y + -1y2 = 0 + 2y2 + -2y2
8 + 2y + -1y2 = 2y2 + -2y2

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

Factor a trinomial.
(4 + -1y)(2 + y) = 0


Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {4, -2}

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