-5(y+4)(2*y)(6y-18)=0

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Solution for -5(y+4)(2*y)(6y-18)=0 equation: 


Simplifying
-5(y + 4)(2y)(6y + -18) = 0

Reorder the terms:
-5(4 + y)(2y)(6y + -18) = 0

Remove parenthesis around (2y)
-5(4 + y) * 2y(6y + -18) = 0

Reorder the terms:
-5(4 + y) * 2y(-18 + 6y) = 0

Reorder the terms for easier multiplication:
-5 * 2y(4 + y)(-18 + 6y) = 0

Multiply -5 * 2
-10y(4 + y)(-18 + 6y) = 0

Multiply (4 + y) * (-18 + 6y)
-10y(4(-18 + 6y) + y(-18 + 6y)) = 0
-10y((-18 * 4 + 6y * 4) + y(-18 + 6y)) = 0
-10y((-72 + 24y) + y(-18 + 6y)) = 0
-10y(-72 + 24y + (-18 * y + 6y * y)) = 0
-10y(-72 + 24y + (-18y + 6y2)) = 0

Combine like terms: 24y + -18y = 6y
-10y(-72 + 6y + 6y2) = 0
(-72 * -10y + 6y * -10y + 6y2 * -10y) = 0
(720y + -60y2 + -60y3) = 0

Solving
720y + -60y2 + -60y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '60y'.
60y(12 + -1y + -1y2) = 0

Factor a trinomial.
60y((3 + -1y)(4 + y)) = 0

Ignore the factor 60.

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 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3

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, 3, -4}

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