-4y(y+2)(y+5)=0

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Solution for -4y(y+2)(y+5)=0 equation: 


Simplifying
-4y(y + 2)(y + 5) = 0

Reorder the terms:
-4y(2 + y)(y + 5) = 0

Reorder the terms:
-4y(2 + y)(5 + y) = 0

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

Combine like terms: 2y + 5y = 7y
-4y(10 + 7y + y2) = 0
(10 * -4y + 7y * -4y + y2 * -4y) = 0
(-40y + -28y2 + -4y3) = 0

Solving
-40y + -28y2 + -4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-4y'.
-4y(10 + 7y + y2) = 0

Factor a trinomial.
-4y((5 + y)(2 + 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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {0, -5, -2}

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