12p^4+61p^3q+5p^2q^2=

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Solution for 12p^4+61p^3q+5p^2q^2= equation: 


Simplifying
12p4 + 61p3q + 5p2q2 = 0

Reorder the terms:
5p2q2 + 61p3q + 12p4 = 0

Solving
5p2q2 + 61p3q + 12p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(5q2 + 61pq + 12p2) = 0

Factor a trinomial.
p2((5q + p)(q + 12p)) = 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 '(5q + p)' equal to zero and attempt to solve:

Simplifying
5q + p = 0

Reorder the terms:
p + 5q = 0

Solving
p + 5q = 0

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

Add '-5q' to each side of the equation.
p + 5q + -5q = 0 + -5q

Combine like terms: 5q + -5q = 0
p + 0 = 0 + -5q
p = 0 + -5q
Remove the zero:
p = -5q

Simplifying
p = -5q

Subproblem 3
Set the factor '(q + 12p)' equal to zero and attempt to solve:

Simplifying
q + 12p = 0

Reorder the terms:
12p + q = 0

Solving
12p + q = 0

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

Add '-1q' to each side of the equation.
12p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
12p + 0 = 0 + -1q
12p = 0 + -1q
Remove the zero:
12p = -1q

Divide each side by '12'.
p = -0.08333333333q

Simplifying
p = -0.08333333333q
Solution
p = {0, -5q, -0.08333333333q}

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