5y(y+9)=6(y+9)

Solution for 5y(y+9)=6(y+9) equation:

Simplifying
5y(y + 9) = 6(y + 9)

Reorder the terms:
5y(9 + y) = 6(y + 9)
(9 * 5y + y * 5y) = 6(y + 9)
(45y + 5y2) = 6(y + 9)

Reorder the terms:
45y + 5y2 = 6(9 + y)
45y + 5y2 = (9 * 6 + y * 6)
45y + 5y2 = (54 + 6y)

Solving
45y + 5y2 = 54 + 6y

Solving for variable 'y'.

Reorder the terms:
-54 + 45y + -6y + 5y2 = 54 + 6y + -54 + -6y

Combine like terms: 45y + -6y = 39y
-54 + 39y + 5y2 = 54 + 6y + -54 + -6y

Reorder the terms:
-54 + 39y + 5y2 = 54 + -54 + 6y + -6y

Combine like terms: 54 + -54 = 0
-54 + 39y + 5y2 = 0 + 6y + -6y
-54 + 39y + 5y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-54 + 39y + 5y2 = 0

Factor a trinomial.
(-9 + -1y)(6 + -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 '(6 + -5y)' equal to zero and attempt to solve:

Simplifying
6 + -5y = 0

Solving
6 + -5y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5y = 0 + -6
-5y = 0 + -6

Combine like terms: 0 + -6 = -6
-5y = -6

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {-9, 1.2}