36p^2xy-120p^2rx^2-144p^2x^3+30p^2ry=0

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Solution for 36p^2xy-120p^2rx^2-144p^2x^3+30p^2ry=0 equation: 


Simplifying
36p2xy + -120p2rx2 + -144p2x3 + 30p2ry = 0

Reorder the terms:
-120p2rx2 + 30p2ry + 36p2xy + -144p2x3 = 0

Solving
-120p2rx2 + 30p2ry + 36p2xy + -144p2x3 = 0

Solving for variable 'p'.

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

Factor out the Greatest Common Factor (GCF), '6p2'.
6p2(-20rx2 + 5ry + 6xy + -24x3) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

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

Subproblem 2
Set the factor '(-20rx2 + 5ry + 6xy + -24x3)' equal to zero and attempt to solve:

Simplifying
-20rx2 + 5ry + 6xy + -24x3 = 0

Solving
-20rx2 + 5ry + 6xy + -24x3 = 0

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

Add '20rx2' to each side of the equation.
-20rx2 + 5ry + 6xy + 20rx2 + -24x3 = 0 + 20rx2

Reorder the terms:
-20rx2 + 20rx2 + 5ry + 6xy + -24x3 = 0 + 20rx2

Combine like terms: -20rx2 + 20rx2 = 0
0 + 5ry + 6xy + -24x3 = 0 + 20rx2
5ry + 6xy + -24x3 = 0 + 20rx2
Remove the zero:
5ry + 6xy + -24x3 = 20rx2

Add '-5ry' to each side of the equation.
5ry + 6xy + -5ry + -24x3 = 20rx2 + -5ry

Reorder the terms:
5ry + -5ry + 6xy + -24x3 = 20rx2 + -5ry

Combine like terms: 5ry + -5ry = 0
0 + 6xy + -24x3 = 20rx2 + -5ry
6xy + -24x3 = 20rx2 + -5ry

Add '-6xy' to each side of the equation.
6xy + -6xy + -24x3 = 20rx2 + -5ry + -6xy

Combine like terms: 6xy + -6xy = 0
0 + -24x3 = 20rx2 + -5ry + -6xy
-24x3 = 20rx2 + -5ry + -6xy

Add '24x3' to each side of the equation.
-24x3 + 24x3 = 20rx2 + -5ry + -6xy + 24x3

Combine like terms: -24x3 + 24x3 = 0
0 = 20rx2 + -5ry + -6xy + 24x3

Simplifying
0 = 20rx2 + -5ry + -6xy + 24x3

The solution to this equation could not be determined.

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

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