3(y+1)(3y-5)=0

Solution for 3(y+1)(3y-5)=0 equation:

Simplifying
3(y + 1)(3y + -5) = 0

Reorder the terms:
3(1 + y)(3y + -5) = 0

Reorder the terms:
3(1 + y)(-5 + 3y) = 0

Multiply (1 + y) * (-5 + 3y)
3(1(-5 + 3y) + y(-5 + 3y)) = 0
3((-5 * 1 + 3y * 1) + y(-5 + 3y)) = 0
3((-5 + 3y) + y(-5 + 3y)) = 0
3(-5 + 3y + (-5 * y + 3y * y)) = 0
3(-5 + 3y + (-5y + 3y2)) = 0

Combine like terms: 3y + -5y = -2y
3(-5 + -2y + 3y2) = 0
(-5 * 3 + -2y * 3 + 3y2 * 3) = 0
(-15 + -6y + 9y2) = 0

Solving
-15 + -6y + 9y2 = 0

Solving for variable 'y'.

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

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
y = {-1, 1.666666667}