3y(2y+1)(2y+5)=0

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Solution for 3y(2y+1)(2y+5)=0 equation: 


Simplifying
3y(2y + 1)(2y + 5) = 0

Reorder the terms:
3y(1 + 2y)(2y + 5) = 0

Reorder the terms:
3y(1 + 2y)(5 + 2y) = 0

Multiply (1 + 2y) * (5 + 2y)
3y(1(5 + 2y) + 2y * (5 + 2y)) = 0
3y((5 * 1 + 2y * 1) + 2y * (5 + 2y)) = 0
3y((5 + 2y) + 2y * (5 + 2y)) = 0
3y(5 + 2y + (5 * 2y + 2y * 2y)) = 0
3y(5 + 2y + (10y + 4y2)) = 0

Combine like terms: 2y + 10y = 12y
3y(5 + 12y + 4y2) = 0
(5 * 3y + 12y * 3y + 4y2 * 3y) = 0
(15y + 36y2 + 12y3) = 0

Solving
15y + 36y2 + 12y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(5 + 12y + 4y2) = 0

Factor a trinomial.
3y((5 + 2y)(1 + 2y)) = 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 '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 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 + 2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2y = 0 + -5
2y = 0 + -5

Combine like terms: 0 + -5 = -5
2y = -5

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5

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

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {0, -2.5, -0.5}

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