2y^2+16y+30=y^2+10y+25

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Solution for 2y^2+16y+30=y^2+10y+25 equation: 


Simplifying
2y2 + 16y + 30 = y2 + 10y + 25

Reorder the terms:
30 + 16y + 2y2 = y2 + 10y + 25

Reorder the terms:
30 + 16y + 2y2 = 25 + 10y + y2

Solving
30 + 16y + 2y2 = 25 + 10y + y2

Solving for variable 'y'.

Reorder the terms:
30 + -25 + 16y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 30 + -25 = 5
5 + 16y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 16y + -10y = 6y
5 + 6y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
5 + 6y + 1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Reorder the terms:
5 + 6y + 1y2 = 25 + -25 + 10y + -10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
5 + 6y + 1y2 = 0 + 10y + -10y + y2 + -1y2
5 + 6y + 1y2 = 10y + -10y + y2 + -1y2

Combine like terms: 10y + -10y = 0
5 + 6y + 1y2 = 0 + y2 + -1y2
5 + 6y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5 + 6y + 1y2 = 0

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


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

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5

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

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {-5, -1}

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