y(2y+1)=15

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

Simplifying
y(2y + 1) = 15

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

Solving
1y + 2y2 = 15

Solving for variable 'y'.

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

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

Factor a trinomial.
(-3 + -1y)(5 + -2y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-3, 2.5}