3y(7y+4)(6y+5)=0

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Solution for 3y(7y+4)(6y+5)=0 equation: 


Simplifying
3y(7y + 4)(6y + 5) = 0

Reorder the terms:
3y(4 + 7y)(6y + 5) = 0

Reorder the terms:
3y(4 + 7y)(5 + 6y) = 0

Multiply (4 + 7y) * (5 + 6y)
3y(4(5 + 6y) + 7y * (5 + 6y)) = 0
3y((5 * 4 + 6y * 4) + 7y * (5 + 6y)) = 0
3y((20 + 24y) + 7y * (5 + 6y)) = 0
3y(20 + 24y + (5 * 7y + 6y * 7y)) = 0
3y(20 + 24y + (35y + 42y2)) = 0

Combine like terms: 24y + 35y = 59y
3y(20 + 59y + 42y2) = 0
(20 * 3y + 59y * 3y + 42y2 * 3y) = 0
(60y + 177y2 + 126y3) = 0

Solving
60y + 177y2 + 126y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(20 + 59y + 42y2) = 0

Factor a trinomial.
3y((5 + 6y)(4 + 7y)) = 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 '(5 + 6y)' equal to zero and attempt to solve:

Simplifying
5 + 6y = 0

Solving
5 + 6y = 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 + 6y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6y = 0 + -5
6y = 0 + -5

Combine like terms: 0 + -5 = -5
6y = -5

Divide each side by '6'.
y = -0.8333333333

Simplifying
y = -0.8333333333

Subproblem 3
Set the factor '(4 + 7y)' equal to zero and attempt to solve:

Simplifying
4 + 7y = 0

Solving
4 + 7y = 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 + 7y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7y = 0 + -4
7y = 0 + -4

Combine like terms: 0 + -4 = -4
7y = -4

Divide each side by '7'.
y = -0.5714285714

Simplifying
y = -0.5714285714
Solution
y = {0, -0.8333333333, -0.5714285714}

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