4y(y+9)=3(y+9)

Solution for 4y(y+9)=3(y+9) equation:

Simplifying
4y(y + 9) = 3(y + 9)

Reorder the terms:
4y(9 + y) = 3(y + 9)
(9 * 4y + y * 4y) = 3(y + 9)
(36y + 4y2) = 3(y + 9)

Reorder the terms:
36y + 4y2 = 3(9 + y)
36y + 4y2 = (9 * 3 + y * 3)
36y + 4y2 = (27 + 3y)

Solving
36y + 4y2 = 27 + 3y

Solving for variable 'y'.

Reorder the terms:
-27 + 36y + -3y + 4y2 = 27 + 3y + -27 + -3y

Combine like terms: 36y + -3y = 33y
-27 + 33y + 4y2 = 27 + 3y + -27 + -3y

Reorder the terms:
-27 + 33y + 4y2 = 27 + -27 + 3y + -3y

Combine like terms: 27 + -27 = 0
-27 + 33y + 4y2 = 0 + 3y + -3y
-27 + 33y + 4y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-27 + 33y + 4y2 = 0

Factor a trinomial.
(-9 + -1y)(3 + -4y) = 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 '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 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 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-9, 0.75}