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

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

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

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

Multiply (6 + y) * (3 + -5y)
5(6(3 + -5y) + y(3 + -5y)) = 0
5((3 * 6 + -5y * 6) + y(3 + -5y)) = 0
5((18 + -30y) + y(3 + -5y)) = 0
5(18 + -30y + (3 * y + -5y * y)) = 0
5(18 + -30y + (3y + -5y2)) = 0

Combine like terms: -30y + 3y = -27y
5(18 + -27y + -5y2) = 0
(18 * 5 + -27y * 5 + -5y2 * 5) = 0
(90 + -135y + -25y2) = 0

Solving
90 + -135y + -25y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + -27y + -5y2) = 0

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

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

Simplifying
3 + -5y = 0

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

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

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

Divide each side by '-5'.
y = 0.6

Simplifying
y = 0.6
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Solution
y = {0.6, -6}