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

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


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

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

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

Remove parenthesis around (36 + -12y + y2)
28 + -14y + 2y2 = 36 + -12y + y2

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

Solving for variable 'y'.

Reorder the terms:
28 + -36 + -14y + 12y + 2y2 + -1y2 = 36 + -12y + y2 + -36 + 12y + -1y2

Combine like terms: 28 + -36 = -8
-8 + -14y + 12y + 2y2 + -1y2 = 36 + -12y + y2 + -36 + 12y + -1y2

Combine like terms: -14y + 12y = -2y
-8 + -2y + 2y2 + -1y2 = 36 + -12y + y2 + -36 + 12y + -1y2

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

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

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

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

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

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


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2

Subproblem 2
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
Solution
y = {-2, 4}

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