9y(5y-4)(4y-5)=0

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Solution for 9y(5y-4)(4y-5)=0 equation: 


Simplifying
9y(5y + -4)(4y + -5) = 0

Reorder the terms:
9y(-4 + 5y)(4y + -5) = 0

Reorder the terms:
9y(-4 + 5y)(-5 + 4y) = 0

Multiply (-4 + 5y) * (-5 + 4y)
9y(-4(-5 + 4y) + 5y * (-5 + 4y)) = 0
9y((-5 * -4 + 4y * -4) + 5y * (-5 + 4y)) = 0
9y((20 + -16y) + 5y * (-5 + 4y)) = 0
9y(20 + -16y + (-5 * 5y + 4y * 5y)) = 0
9y(20 + -16y + (-25y + 20y2)) = 0

Combine like terms: -16y + -25y = -41y
9y(20 + -41y + 20y2) = 0
(20 * 9y + -41y * 9y + 20y2 * 9y) = 0
(180y + -369y2 + 180y3) = 0

Solving
180y + -369y2 + 180y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9y'.
9y(20 + -41y + 20y2) = 0

Factor a trinomial.
9y((4 + -5y)(5 + -4y)) = 0

Ignore the factor 9.

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 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 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 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8

Subproblem 3
Set the factor '(5 + -4y)' equal to zero and attempt to solve:

Simplifying
5 + -4y = 0

Solving
5 + -4y = 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 + -4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4y = 0 + -5
-4y = 0 + -5

Combine like terms: 0 + -5 = -5
-4y = -5

Divide each side by '-4'.
y = 1.25

Simplifying
y = 1.25
Solution
y = {0, 0.8, 1.25}

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