p^5(p^2-pq-2q^2)=0

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Solution for p^5(p^2-pq-2q^2)=0 equation: 


Simplifying
p5(p2 + -1pq + -2q2) = 0

Reorder the terms:
p5(-1pq + p2 + -2q2) = 0
(-1pq * p5 + p2 * p5 + -2q2 * p5) = 0

Reorder the terms:
(-2p5q2 + -1p6q + p7) = 0
(-2p5q2 + -1p6q + p7) = 0

Solving
-2p5q2 + -1p6q + p7 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p5'.
p5(-2q2 + -1pq + p2) = 0

Factor a trinomial.
p5((-1q + -1p)(2q + -1p)) = 0


Subproblem 1
Set the factor 'p5' equal to zero and attempt to solve:

Simplifying
p5 = 0

Solving
p5 = 0

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

Simplifying
p5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1q + -1p)' equal to zero and attempt to solve:

Simplifying
-1q + -1p = 0

Reorder the terms:
-1p + -1q = 0

Solving
-1p + -1q = 0

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

Add 'q' to each side of the equation.
-1p + -1q + q = 0 + q

Combine like terms: -1q + q = 0
-1p + 0 = 0 + q
-1p = 0 + q
Remove the zero:
-1p = q

Divide each side by '-1'.
p = -1q

Simplifying
p = -1q

Subproblem 3
Set the factor '(2q + -1p)' equal to zero and attempt to solve:

Simplifying
2q + -1p = 0

Reorder the terms:
-1p + 2q = 0

Solving
-1p + 2q = 0

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

Add '-2q' to each side of the equation.
-1p + 2q + -2q = 0 + -2q

Combine like terms: 2q + -2q = 0
-1p + 0 = 0 + -2q
-1p = 0 + -2q
Remove the zero:
-1p = -2q

Divide each side by '-1'.
p = 2q

Simplifying
p = 2q
Solution
p = {-1q, 2q}

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