(5y^2)2y(y+6)(y+9)=

Solution for (5y^2)2y(y+6)(y+9)= equation:

Simplifying
(5y2) * 2y(y + 6)(y + 9) = 0

Remove parenthesis around (5y2)
5y2 * 2y(y + 6)(y + 9) = 0

Reorder the terms:
5y2 * 2y(6 + y)(y + 9) = 0

Reorder the terms:
5y2 * 2y(6 + y)(9 + y) = 0

Reorder the terms for easier multiplication:
5 * 2y2 * y(6 + y)(9 + y) = 0

Multiply 5 * 2
10y2 * y(6 + y)(9 + y) = 0

Multiply y2 * y
10y3(6 + y)(9 + y) = 0

Multiply (6 + y) * (9 + y)
10y3(6(9 + y) + y(9 + y)) = 0
10y3((9 * 6 + y * 6) + y(9 + y)) = 0
10y3((54 + 6y) + y(9 + y)) = 0
10y3(54 + 6y + (9 * y + y * y)) = 0
10y3(54 + 6y + (9y + y2)) = 0

Combine like terms: 6y + 9y = 15y
10y3(54 + 15y + y2) = 0
(54 * 10y3 + 15y * 10y3 + y2 * 10y3) = 0
(540y3 + 150y4 + 10y5) = 0

Solving
540y3 + 150y4 + 10y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '10y3'.
10y3(54 + 15y + y2) = 0

Factor a trinomial.
10y3((9 + y)(6 + y)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 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 + y = 0 + -9

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

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

Simplifying
y = -9
Subproblem 3
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 = {-9, -6}