-5y(y-3)(y-2)=0

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Solution for -5y(y-3)(y-2)=0 equation: 


Simplifying
-5y(y + -3)(y + -2) = 0

Reorder the terms:
-5y(-3 + y)(y + -2) = 0

Reorder the terms:
-5y(-3 + y)(-2 + y) = 0

Multiply (-3 + y) * (-2 + y)
-5y(-3(-2 + y) + y(-2 + y)) = 0
-5y((-2 * -3 + y * -3) + y(-2 + y)) = 0
-5y((6 + -3y) + y(-2 + y)) = 0
-5y(6 + -3y + (-2 * y + y * y)) = 0
-5y(6 + -3y + (-2y + y2)) = 0

Combine like terms: -3y + -2y = -5y
-5y(6 + -5y + y2) = 0
(6 * -5y + -5y * -5y + y2 * -5y) = 0
(-30y + 25y2 + -5y3) = 0

Solving
-30y + 25y2 + -5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-6 + 5y + -1y2) = 0

Factor a trinomial.
5y((-3 + y)(2 + -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 '(-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

Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0, 3, 2}

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