4y(9y+6)=60

Solution for 4y(9y+6)=60 equation:

Simplifying
4y(9y + 6) = 60

Reorder the terms:
4y(6 + 9y) = 60
(6 * 4y + 9y * 4y) = 60
(24y + 36y2) = 60

Solving
24y + 36y2 = 60

Solving for variable 'y'.

Reorder the terms:
-60 + 24y + 36y2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 24y + 36y2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-5 + 2y + 3y2) = 0

Factor a trinomial.
12((-5 + -3y)(1 + -1y)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-5 + -3y)' equal to zero and attempt to solve:

Simplifying
-5 + -3y = 0

Solving
-5 + -3y = 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 + -3y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y = 0 + 5
-3y = 0 + 5

Combine like terms: 0 + 5 = 5
-3y = 5

Divide each side by '-3'.
y = -1.666666667

Simplifying
y = -1.666666667
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-1.666666667, 1}