13p^4+40p^3q+3p^2q^2=0

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Solution for 13p^4+40p^3q+3p^2q^2=0 equation: 


Simplifying
13p4 + 40p3q + 3p2q2 = 0

Reorder the terms:
3p2q2 + 40p3q + 13p4 = 0

Solving
3p2q2 + 40p3q + 13p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(3q2 + 40pq + 13p2) = 0

Factor a trinomial.
p2((3q + 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 '(3q + p)' equal to zero and attempt to solve:

Simplifying
3q + p = 0

Reorder the terms:
p + 3q = 0

Solving
p + 3q = 0

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

Add '-3q' to each side of the equation.
p + 3q + -3q = 0 + -3q

Combine like terms: 3q + -3q = 0
p + 0 = 0 + -3q
p = 0 + -3q
Remove the zero:
p = -3q

Simplifying
p = -3q

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, -3q, -0.07692307692q}

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