3y(3y+1)(9y+2)=0

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Solution for 3y(3y+1)(9y+2)=0 equation: 


Simplifying
3y(3y + 1)(9y + 2) = 0

Reorder the terms:
3y(1 + 3y)(9y + 2) = 0

Reorder the terms:
3y(1 + 3y)(2 + 9y) = 0

Multiply (1 + 3y) * (2 + 9y)
3y(1(2 + 9y) + 3y * (2 + 9y)) = 0
3y((2 * 1 + 9y * 1) + 3y * (2 + 9y)) = 0
3y((2 + 9y) + 3y * (2 + 9y)) = 0
3y(2 + 9y + (2 * 3y + 9y * 3y)) = 0
3y(2 + 9y + (6y + 27y2)) = 0

Combine like terms: 9y + 6y = 15y
3y(2 + 15y + 27y2) = 0
(2 * 3y + 15y * 3y + 27y2 * 3y) = 0
(6y + 45y2 + 81y3) = 0

Solving
6y + 45y2 + 81y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(2 + 15y + 27y2) = 0

Factor a trinomial.
3y((1 + 3y)(2 + 9y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
1 + 3y = 0

Solving
1 + 3y = 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 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333

Subproblem 3
Set the factor '(2 + 9y)' equal to zero and attempt to solve:

Simplifying
2 + 9y = 0

Solving
2 + 9y = 0

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

Add '-2' to each side of the equation.
2 + -2 + 9y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9y = 0 + -2
9y = 0 + -2

Combine like terms: 0 + -2 = -2
9y = -2

Divide each side by '9'.
y = -0.2222222222

Simplifying
y = -0.2222222222
Solution
y = {0, -0.3333333333, -0.2222222222}

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