y(9+y)=4(2y+5)

Solution for y(9+y)=4(2y+5) equation:

Simplifying
y(9 + y) = 4(2y + 5)
(9 * y + y * y) = 4(2y + 5)
(9y + y2) = 4(2y + 5)

Reorder the terms:
9y + y2 = 4(5 + 2y)
9y + y2 = (5 * 4 + 2y * 4)
9y + y2 = (20 + 8y)

Solving
9y + y2 = 20 + 8y

Solving for variable 'y'.

Reorder the terms:
-20 + 9y + -8y + y2 = 20 + 8y + -20 + -8y

Combine like terms: 9y + -8y = 1y
-20 + 1y + y2 = 20 + 8y + -20 + -8y

Reorder the terms:
-20 + 1y + y2 = 20 + -20 + 8y + -8y

Combine like terms: 20 + -20 = 0
-20 + 1y + y2 = 0 + 8y + -8y
-20 + 1y + y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-20 + 1y + y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-5, 4}