y^2+8y+16=2y^2+6y+1

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Solution for y^2+8y+16=2y^2+6y+1 equation: 


Simplifying
y2 + 8y + 16 = 2y2 + 6y + 1

Reorder the terms:
16 + 8y + y2 = 2y2 + 6y + 1

Reorder the terms:
16 + 8y + y2 = 1 + 6y + 2y2

Solving
16 + 8y + y2 = 1 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
16 + -1 + 8y + -6y + y2 + -2y2 = 1 + 6y + 2y2 + -1 + -6y + -2y2

Combine like terms: 16 + -1 = 15
15 + 8y + -6y + y2 + -2y2 = 1 + 6y + 2y2 + -1 + -6y + -2y2

Combine like terms: 8y + -6y = 2y
15 + 2y + y2 + -2y2 = 1 + 6y + 2y2 + -1 + -6y + -2y2

Combine like terms: y2 + -2y2 = -1y2
15 + 2y + -1y2 = 1 + 6y + 2y2 + -1 + -6y + -2y2

Reorder the terms:
15 + 2y + -1y2 = 1 + -1 + 6y + -6y + 2y2 + -2y2

Combine like terms: 1 + -1 = 0
15 + 2y + -1y2 = 0 + 6y + -6y + 2y2 + -2y2
15 + 2y + -1y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
15 + 2y + -1y2 = 0 + 2y2 + -2y2
15 + 2y + -1y2 = 2y2 + -2y2

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

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


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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

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 = {5, -3}

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