y=5xy^2(4x^3-7xy+y^2)

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Solution for y=5xy^2(4x^3-7xy+y^2) equation:


Simplifying
y = 5xy2(4x3 + -7xy + y2)

Reorder the terms:
y = 5xy2(-7xy + 4x3 + y2)
y = (-7xy * 5xy2 + 4x3 * 5xy2 + y2 * 5xy2)

Reorder the terms:
y = (5xy4 + -35x2y3 + 20x4y2)
y = (5xy4 + -35x2y3 + 20x4y2)

Solving
y = 5xy4 + -35x2y3 + 20x4y2

Solving for variable 'y'.

Reorder the terms:
-5xy4 + 35x2y3 + -20x4y2 + y = 5xy4 + -35x2y3 + 20x4y2 + -5xy4 + 35x2y3 + -20x4y2

Reorder the terms:
-5xy4 + 35x2y3 + -20x4y2 + y = 5xy4 + -5xy4 + -35x2y3 + 35x2y3 + 20x4y2 + -20x4y2

Combine like terms: 5xy4 + -5xy4 = 0
-5xy4 + 35x2y3 + -20x4y2 + y = 0 + -35x2y3 + 35x2y3 + 20x4y2 + -20x4y2
-5xy4 + 35x2y3 + -20x4y2 + y = -35x2y3 + 35x2y3 + 20x4y2 + -20x4y2

Combine like terms: -35x2y3 + 35x2y3 = 0
-5xy4 + 35x2y3 + -20x4y2 + y = 0 + 20x4y2 + -20x4y2
-5xy4 + 35x2y3 + -20x4y2 + y = 20x4y2 + -20x4y2

Combine like terms: 20x4y2 + -20x4y2 = 0
-5xy4 + 35x2y3 + -20x4y2 + y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-5xy3 + 35x2y2 + -20x4y + 1) = 0

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 '(-5xy3 + 35x2y2 + -20x4y + 1)' equal to zero and attempt to solve: Simplifying -5xy3 + 35x2y2 + -20x4y + 1 = 0 Reorder the terms: 1 + -5xy3 + 35x2y2 + -20x4y = 0 Solving 1 + -5xy3 + 35x2y2 + -20x4y = 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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