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

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


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

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

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

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

Combine like terms: 10y + -21y = -11y
2y(-35 + -11y + 6y2) = 0
(-35 * 2y + -11y * 2y + 6y2 * 2y) = 0
(-70y + -22y2 + 12y3) = 0

Solving
-70y + -22y2 + 12y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-35 + -11y + 6y2) = 0

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

Ignore the factor 2.

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 '(-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

Subproblem 3
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
Solution
y = {0, -1.666666667, 3.5}

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