(4y^2+y)(2y^3+3y^2+y)=0

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Solution for (4y^2+y)(2y^3+3y^2+y)=0 equation: 


Simplifying
(4y2 + y)(2y3 + 3y2 + y) = 0

Reorder the terms:
(y + 4y2)(2y3 + 3y2 + y) = 0

Reorder the terms:
(y + 4y2)(y + 3y2 + 2y3) = 0

Multiply (y + 4y2) * (y + 3y2 + 2y3)
(y(y + 3y2 + 2y3) + 4y2 * (y + 3y2 + 2y3)) = 0
((y * y + 3y2 * y + 2y3 * y) + 4y2 * (y + 3y2 + 2y3)) = 0
((y2 + 3y3 + 2y4) + 4y2 * (y + 3y2 + 2y3)) = 0
(y2 + 3y3 + 2y4 + (y * 4y2 + 3y2 * 4y2 + 2y3 * 4y2)) = 0
(y2 + 3y3 + 2y4 + (4y3 + 12y4 + 8y5)) = 0

Reorder the terms:
(y2 + 3y3 + 4y3 + 2y4 + 12y4 + 8y5) = 0

Combine like terms: 3y3 + 4y3 = 7y3
(y2 + 7y3 + 2y4 + 12y4 + 8y5) = 0

Combine like terms: 2y4 + 12y4 = 14y4
(y2 + 7y3 + 14y4 + 8y5) = 0

Solving
y2 + 7y3 + 14y4 + 8y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(1 + 7y + 14y2 + 8y3) = 0


Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

Subproblem 2
Set the factor '(1 + 7y + 14y2 + 8y3)' equal to zero and attempt to solve:

Simplifying
1 + 7y + 14y2 + 8y3 = 0

Solving
1 + 7y + 14y2 + 8y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}

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