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

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


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

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

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

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

Combine like terms: -4y + -5y = -9y
5y(20 + -9y + y2) = 0
(20 * 5y + -9y * 5y + y2 * 5y) = 0
(100y + -45y2 + 5y3) = 0

Solving
100y + -45y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(20 + -9y + y2) = 0

Factor a trinomial.
5y((4 + -1y)(5 + -1y)) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

Subproblem 3
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {0, 4, 5}

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