4y(3y+1)(7y+5)=0

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Solution for 4y(3y+1)(7y+5)=0 equation: 


Simplifying
4y(3y + 1)(7y + 5) = 0

Reorder the terms:
4y(1 + 3y)(7y + 5) = 0

Reorder the terms:
4y(1 + 3y)(5 + 7y) = 0

Multiply (1 + 3y) * (5 + 7y)
4y(1(5 + 7y) + 3y * (5 + 7y)) = 0
4y((5 * 1 + 7y * 1) + 3y * (5 + 7y)) = 0
4y((5 + 7y) + 3y * (5 + 7y)) = 0
4y(5 + 7y + (5 * 3y + 7y * 3y)) = 0
4y(5 + 7y + (15y + 21y2)) = 0

Combine like terms: 7y + 15y = 22y
4y(5 + 22y + 21y2) = 0
(5 * 4y + 22y * 4y + 21y2 * 4y) = 0
(20y + 88y2 + 84y3) = 0

Solving
20y + 88y2 + 84y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(5 + 22y + 21y2) = 0

Factor a trinomial.
4y((5 + 7y)(1 + 3y)) = 0

Ignore the factor 4.

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

Simplifying
5 + 7y = 0

Solving
5 + 7y = 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 + 7y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7y = 0 + -5
7y = 0 + -5

Combine like terms: 0 + -5 = -5
7y = -5

Divide each side by '7'.
y = -0.7142857143

Simplifying
y = -0.7142857143

Subproblem 3
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {0, -0.7142857143, -0.3333333333}

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