-5y(y-9)(3y+2)=0

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Solution for -5y(y-9)(3y+2)=0 equation: 


Simplifying
-5y(y + -9)(3y + 2) = 0

Reorder the terms:
-5y(-9 + y)(3y + 2) = 0

Reorder the terms:
-5y(-9 + y)(2 + 3y) = 0

Multiply (-9 + y) * (2 + 3y)
-5y(-9(2 + 3y) + y(2 + 3y)) = 0
-5y((2 * -9 + 3y * -9) + y(2 + 3y)) = 0
-5y((-18 + -27y) + y(2 + 3y)) = 0
-5y(-18 + -27y + (2 * y + 3y * y)) = 0
-5y(-18 + -27y + (2y + 3y2)) = 0

Combine like terms: -27y + 2y = -25y
-5y(-18 + -25y + 3y2) = 0
(-18 * -5y + -25y * -5y + 3y2 * -5y) = 0
(90y + 125y2 + -15y3) = 0

Solving
90y + 125y2 + -15y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(18 + 25y + -3y2) = 0

Factor a trinomial.
5y((9 + -1y)(2 + 3y)) = 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 '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9

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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {0, 9, -0.6666666667}

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