p^2(13p^2+27pq+2q^2)=0

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Solution for p^2(13p^2+27pq+2q^2)=0 equation: 


Simplifying
p2(13p2 + 27pq + 2q2) = 0

Reorder the terms:
p2(27pq + 13p2 + 2q2) = 0
(27pq * p2 + 13p2 * p2 + 2q2 * p2) = 0

Reorder the terms:
(2p2q2 + 27p3q + 13p4) = 0
(2p2q2 + 27p3q + 13p4) = 0

Solving
2p2q2 + 27p3q + 13p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(2q2 + 27pq + 13p2) = 0

Factor a trinomial.
p2((2q + p)(q + 13p)) = 0


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 '(2q + p)' equal to zero and attempt to solve:

Simplifying
2q + p = 0

Reorder the terms:
p + 2q = 0

Solving
p + 2q = 0

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

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

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

Simplifying
p = -2q

Subproblem 3
Set the factor '(q + 13p)' equal to zero and attempt to solve:

Simplifying
q + 13p = 0

Reorder the terms:
13p + q = 0

Solving
13p + q = 0

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

Add '-1q' to each side of the equation.
13p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
13p + 0 = 0 + -1q
13p = 0 + -1q
Remove the zero:
13p = -1q

Divide each side by '13'.
p = -0.07692307692q

Simplifying
p = -0.07692307692q
Solution
p = {0, -2q, -0.07692307692q}

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