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

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


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

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

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

Multiply (5 + y) * (4 + y)
y(5(4 + y) + y(4 + y)) = 0
y((4 * 5 + y * 5) + y(4 + y)) = 0
y((20 + 5y) + y(4 + y)) = 0
y(20 + 5y + (4 * y + y * y)) = 0
y(20 + 5y + (4y + y2)) = 0

Combine like terms: 5y + 4y = 9y
y(20 + 9y + y2) = 0
(20 * y + 9y * y + y2 * y) = 0
(20y + 9y2 + y3) = 0

Solving
20y + 9y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(20 + 9y + y2) = 0

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


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 '(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
Solution
y = {0, -5, -4}

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