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

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


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

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

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

Multiply (3 + y) * (5 + y)
-4y(3(5 + y) + y(5 + y)) = 0
-4y((5 * 3 + y * 3) + y(5 + y)) = 0
-4y((15 + 3y) + y(5 + y)) = 0
-4y(15 + 3y + (5 * y + y * y)) = 0
-4y(15 + 3y + (5y + y2)) = 0

Combine like terms: 3y + 5y = 8y
-4y(15 + 8y + y2) = 0
(15 * -4y + 8y * -4y + y2 * -4y) = 0
(-60y + -32y2 + -4y3) = 0

Solving
-60y + -32y2 + -4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-4y'.
-4y(15 + 8y + y2) = 0

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

Ignore the factor -4.

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 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5

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, -5, -3}

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