y(2y+5)=2(36-y)

Solution for y(2y+5)=2(36-y) equation:

Simplifying
y(2y + 5) = 2(36 + -1y)

Reorder the terms:
y(5 + 2y) = 2(36 + -1y)
(5 * y + 2y * y) = 2(36 + -1y)
(5y + 2y2) = 2(36 + -1y)
5y + 2y2 = (36 * 2 + -1y * 2)
5y + 2y2 = (72 + -2y)

Solving
5y + 2y2 = 72 + -2y

Solving for variable 'y'.

Reorder the terms:
-72 + 5y + 2y + 2y2 = 72 + -2y + -72 + 2y

Combine like terms: 5y + 2y = 7y
-72 + 7y + 2y2 = 72 + -2y + -72 + 2y

Reorder the terms:
-72 + 7y + 2y2 = 72 + -72 + -2y + 2y

Combine like terms: 72 + -72 = 0
-72 + 7y + 2y2 = 0 + -2y + 2y
-72 + 7y + 2y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-72 + 7y + 2y2 = 0

Factor a trinomial.
(-8 + -1y)(9 + -2y) = 0

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(9 + -2y)' equal to zero and attempt to solve:

Simplifying
9 + -2y = 0

Solving
9 + -2y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2y = 0 + -9
-2y = 0 + -9

Combine like terms: 0 + -9 = -9
-2y = -9

Divide each side by '-2'.
y = 4.5

Simplifying
y = 4.5
Solution
y = {-8, 4.5}