2y^2+2y+9=y^2+8y+16

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Solution for 2y^2+2y+9=y^2+8y+16 equation: 


Simplifying
2y2 + 2y + 9 = y2 + 8y + 16

Reorder the terms:
9 + 2y + 2y2 = y2 + 8y + 16

Reorder the terms:
9 + 2y + 2y2 = 16 + 8y + y2

Solving
9 + 2y + 2y2 = 16 + 8y + y2

Solving for variable 'y'.

Reorder the terms:
9 + -16 + 2y + -8y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 9 + -16 = -7
-7 + 2y + -8y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 2y + -8y = -6y
-7 + -6y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-7 + -6y + 1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Reorder the terms:
-7 + -6y + 1y2 = 16 + -16 + 8y + -8y + y2 + -1y2

Combine like terms: 16 + -16 = 0
-7 + -6y + 1y2 = 0 + 8y + -8y + y2 + -1y2
-7 + -6y + 1y2 = 8y + -8y + y2 + -1y2

Combine like terms: 8y + -8y = 0
-7 + -6y + 1y2 = 0 + y2 + -1y2
-7 + -6y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-7 + -6y + 1y2 = 0

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


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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1

Subproblem 2
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
Solution
y = {-1, 7}

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