2y(y+1)=y^2+15

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Solution for 2y(y+1)=y^2+15 equation: 


Simplifying
2y(y + 1) = y2 + 15

Reorder the terms:
2y(1 + y) = y2 + 15
(1 * 2y + y * 2y) = y2 + 15
(2y + 2y2) = y2 + 15

Reorder the terms:
2y + 2y2 = 15 + y2

Solving
2y + 2y2 = 15 + y2

Solving for variable 'y'.

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

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

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

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

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

Factor a trinomial.
(-5 + -1y)(3 + -1y) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5, 3}

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