5y(y+4)(y+3)=0

Solution for 5y(y+4)(y+3)=0 equation:

Simplifying
5y(y + 4)(y + 3) = 0

Reorder the terms:
5y(4 + y)(y + 3) = 0

Reorder the terms:
5y(4 + y)(3 + y) = 0

Multiply (4 + y) * (3 + y)
5y(4(3 + y) + y(3 + y)) = 0
5y((3 * 4 + y * 4) + y(3 + y)) = 0
5y((12 + 4y) + y(3 + y)) = 0
5y(12 + 4y + (3 * y + y * y)) = 0
5y(12 + 4y + (3y + y2)) = 0

Combine like terms: 4y + 3y = 7y
5y(12 + 7y + y2) = 0
(12 * 5y + 7y * 5y + y2 * 5y) = 0
(60y + 35y2 + 5y3) = 0

Solving
60y + 35y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(12 + 7y + y2) = 0

Factor a trinomial.
5y((4 + y)(3 + y)) = 0

Ignore the factor 5.
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 '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Subproblem 3
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

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

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

Simplifying
y = -3
Solution
y = {0, -4, -3}