20p^4+18p^2=-39p^3

Solution for 20p^4+18p^2=-39p^3 equation:

Simplifying
20p4 + 18p2 = -39p3

Reorder the terms:
18p2 + 20p4 = -39p3

Solving
18p2 + 20p4 = -39p3

Solving for variable 'p'.

Reorder the terms:
18p2 + 39p3 + 20p4 = -39p3 + 39p3

Combine like terms: -39p3 + 39p3 = 0
18p2 + 39p3 + 20p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(18 + 39p + 20p2) = 0

Factor a trinomial.
p2((6 + 5p)(3 + 4p)) = 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 '(6 + 5p)' equal to zero and attempt to solve:

Simplifying
6 + 5p = 0

Solving
6 + 5p = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5p = 0 + -6
5p = 0 + -6

Combine like terms: 0 + -6 = -6
5p = -6

Divide each side by '5'.
p = -1.2

Simplifying
p = -1.2
Subproblem 3
Set the factor '(3 + 4p)' equal to zero and attempt to solve:

Simplifying
3 + 4p = 0

Solving
3 + 4p = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4p = 0 + -3
4p = 0 + -3

Combine like terms: 0 + -3 = -3
4p = -3

Divide each side by '4'.
p = -0.75

Simplifying
p = -0.75
Solution
p = {0, -1.2, -0.75}