6(y+3)(6-5y)=0

Solution for 6(y+3)(6-5y)=0 equation:

Simplifying
6(y + 3)(6 + -5y) = 0

Reorder the terms:
6(3 + y)(6 + -5y) = 0

Multiply (3 + y) * (6 + -5y)
6(3(6 + -5y) + y(6 + -5y)) = 0
6((6 * 3 + -5y * 3) + y(6 + -5y)) = 0
6((18 + -15y) + y(6 + -5y)) = 0
6(18 + -15y + (6 * y + -5y * y)) = 0
6(18 + -15y + (6y + -5y2)) = 0

Combine like terms: -15y + 6y = -9y
6(18 + -9y + -5y2) = 0
(18 * 6 + -9y * 6 + -5y2 * 6) = 0
(108 + -54y + -30y2) = 0

Solving
108 + -54y + -30y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -9y + -5y2) = 0

Factor a trinomial.
6((6 + -5y)(3 + y)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Solution
y = {1.2, -3}