e^3x(p-1)+p^3e^2y=0

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Solution for e^3x(p-1)+p^3e^2y=0 equation: 


Simplifying
e3x(p + -1) + p3e2y = 0

Reorder the terms:
e3x(-1 + p) + p3e2y = 0
(-1 * e3x + p * e3x) + p3e2y = 0

Reorder the terms:
(e3px + -1e3x) + p3e2y = 0
(e3px + -1e3x) + p3e2y = 0

Reorder the terms:
e2p3y + e3px + -1e3x = 0

Solving
e2p3y + e3px + -1e3x = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e2'.
e2(p3y + epx + -1ex) = 0


Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve:

Simplifying
e2 = 0

Solving
e2 = 0

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

Simplifying
e2 = 0

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

Subproblem 2
Set the factor '(p3y + epx + -1ex)' equal to zero and attempt to solve:

Simplifying
p3y + epx + -1ex = 0

Reorder the terms:
epx + -1ex + p3y = 0

Solving
epx + -1ex + p3y = 0

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

Add '-1p3y' to each side of the equation.
epx + -1ex + p3y + -1p3y = 0 + -1p3y

Combine like terms: p3y + -1p3y = 0
epx + -1ex + 0 = 0 + -1p3y
epx + -1ex = 0 + -1p3y
Remove the zero:
epx + -1ex = -1p3y

The solution to this equation could not be determined.

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

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