3y(3y-5)(2y+7)=0

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Solution for 3y(3y-5)(2y+7)=0 equation: 


Simplifying
3y(3y + -5)(2y + 7) = 0

Reorder the terms:
3y(-5 + 3y)(2y + 7) = 0

Reorder the terms:
3y(-5 + 3y)(7 + 2y) = 0

Multiply (-5 + 3y) * (7 + 2y)
3y(-5(7 + 2y) + 3y * (7 + 2y)) = 0
3y((7 * -5 + 2y * -5) + 3y * (7 + 2y)) = 0
3y((-35 + -10y) + 3y * (7 + 2y)) = 0
3y(-35 + -10y + (7 * 3y + 2y * 3y)) = 0
3y(-35 + -10y + (21y + 6y2)) = 0

Combine like terms: -10y + 21y = 11y
3y(-35 + 11y + 6y2) = 0
(-35 * 3y + 11y * 3y + 6y2 * 3y) = 0
(-105y + 33y2 + 18y3) = 0

Solving
-105y + 33y2 + 18y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-35 + 11y + 6y2) = 0

Factor a trinomial.
3y((-7 + -2y)(5 + -3y)) = 0

Ignore the factor 3.

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 '(-7 + -2y)' equal to zero and attempt to solve:

Simplifying
-7 + -2y = 0

Solving
-7 + -2y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2y = 0 + 7
-2y = 0 + 7

Combine like terms: 0 + 7 = 7
-2y = 7

Divide each side by '-2'.
y = -3.5

Simplifying
y = -3.5

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

Simplifying
5 + -3y = 0

Solving
5 + -3y = 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 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
Solution
y = {0, -3.5, 1.666666667}

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