(4y+1)(y+1)(4y)=(6y^2-4y)(3y)(h)

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Solution for (4y+1)(y+1)(4y)=(6y^2-4y)(3y)(h) equation: 


Simplifying
(4y + 1)(y + 1)(4y) = (6y2 + -4y)(3y)(h)

Reorder the terms:
(1 + 4y)(y + 1)(4y) = (6y2 + -4y)(3y)(h)

Reorder the terms:
(1 + 4y)(1 + y)(4y) = (6y2 + -4y)(3y)(h)

Remove parenthesis around (4y)
(1 + 4y)(1 + y) * 4y = (6y2 + -4y)(3y)(h)

Reorder the terms for easier multiplication:
4y(1 + 4y)(1 + y) = (6y2 + -4y)(3y)(h)

Multiply (1 + 4y) * (1 + y)
4y(1(1 + y) + 4y * (1 + y)) = (6y2 + -4y)(3y)(h)
4y((1 * 1 + y * 1) + 4y * (1 + y)) = (6y2 + -4y)(3y)(h)
4y((1 + 1y) + 4y * (1 + y)) = (6y2 + -4y)(3y)(h)
4y(1 + 1y + (1 * 4y + y * 4y)) = (6y2 + -4y)(3y)(h)
4y(1 + 1y + (4y + 4y2)) = (6y2 + -4y)(3y)(h)

Combine like terms: 1y + 4y = 5y
4y(1 + 5y + 4y2) = (6y2 + -4y)(3y)(h)
(1 * 4y + 5y * 4y + 4y2 * 4y) = (6y2 + -4y)(3y)(h)
(4y + 20y2 + 16y3) = (6y2 + -4y)(3y)(h)

Reorder the terms:
4y + 20y2 + 16y3 = (-4y + 6y2)(3y)(h)

Remove parenthesis around (3y)
4y + 20y2 + 16y3 = (-4y + 6y2) * 3y(h)

Reorder the terms for easier multiplication:
4y + 20y2 + 16y3 = 3y * h(-4y + 6y2)

Multiply y * h
4y + 20y2 + 16y3 = 3hy(-4y + 6y2)
4y + 20y2 + 16y3 = (-4y * 3hy + 6y2 * 3hy)
4y + 20y2 + 16y3 = (-12hy2 + 18hy3)

Solving
4y + 20y2 + 16y3 = -12hy2 + 18hy3

Solving for variable 'y'.

Reorder the terms:
12hy2 + -18hy3 + 4y + 20y2 + 16y3 = -12hy2 + 18hy3 + 12hy2 + -18hy3

Reorder the terms:
12hy2 + -18hy3 + 4y + 20y2 + 16y3 = -12hy2 + 12hy2 + 18hy3 + -18hy3

Combine like terms: -12hy2 + 12hy2 = 0
12hy2 + -18hy3 + 4y + 20y2 + 16y3 = 0 + 18hy3 + -18hy3
12hy2 + -18hy3 + 4y + 20y2 + 16y3 = 18hy3 + -18hy3

Combine like terms: 18hy3 + -18hy3 = 0
12hy2 + -18hy3 + 4y + 20y2 + 16y3 = 0

Factor out the Greatest Common Factor (GCF), '2y'.
2y(6hy + -9hy2 + 2 + 10y + 8y2) = 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 '(6hy + -9hy2 + 2 + 10y + 8y2)' equal to zero and attempt to solve:

Simplifying
6hy + -9hy2 + 2 + 10y + 8y2 = 0

Reorder the terms:
2 + 6hy + -9hy2 + 10y + 8y2 = 0

Solving
2 + 6hy + -9hy2 + 10y + 8y2 = 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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