3y(2y+9)(5-y)=0

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Solution for 3y(2y+9)(5-y)=0 equation: 


Simplifying
3y(2y + 9)(5 + -1y) = 0

Reorder the terms:
3y(9 + 2y)(5 + -1y) = 0

Multiply (9 + 2y) * (5 + -1y)
3y(9(5 + -1y) + 2y * (5 + -1y)) = 0
3y((5 * 9 + -1y * 9) + 2y * (5 + -1y)) = 0
3y((45 + -9y) + 2y * (5 + -1y)) = 0
3y(45 + -9y + (5 * 2y + -1y * 2y)) = 0
3y(45 + -9y + (10y + -2y2)) = 0

Combine like terms: -9y + 10y = 1y
3y(45 + 1y + -2y2) = 0
(45 * 3y + 1y * 3y + -2y2 * 3y) = 0
(135y + 3y2 + -6y3) = 0

Solving
135y + 3y2 + -6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(45 + y + -2y2) = 0

Factor a trinomial.
3y((5 + -1y)(9 + 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 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

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

Simplifying
9 + 2y = 0

Solving
9 + 2y = 0

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

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

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

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

Divide each side by '2'.
y = -4.5

Simplifying
y = -4.5
Solution
y = {0, 5, -4.5}

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