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

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

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

Reorder the terms:
5y(9 + y) = 4(y + 9)
(9 * 5y + y * 5y) = 4(y + 9)
(45y + 5y2) = 4(y + 9)

Reorder the terms:
45y + 5y2 = 4(9 + y)
45y + 5y2 = (9 * 4 + y * 4)
45y + 5y2 = (36 + 4y)

Solving
45y + 5y2 = 36 + 4y

Solving for variable 'y'.

Reorder the terms:
-36 + 45y + -4y + 5y2 = 36 + 4y + -36 + -4y

Combine like terms: 45y + -4y = 41y
-36 + 41y + 5y2 = 36 + 4y + -36 + -4y

Reorder the terms:
-36 + 41y + 5y2 = 36 + -36 + 4y + -4y

Combine like terms: 36 + -36 = 0
-36 + 41y + 5y2 = 0 + 4y + -4y
-36 + 41y + 5y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-36 + 41y + 5y2 = 0

Factor a trinomial.
(-9 + -1y)(4 + -5y) = 0

Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 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 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 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 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Solution
y = {-9, 0.8}