6p^4+6p^2=-13p^3

Solution for 6p^4+6p^2=-13p^3 equation:

Simplifying
6p4 + 6p2 = -13p3

Reorder the terms:
6p2 + 6p4 = -13p3

Solving
6p2 + 6p4 = -13p3

Solving for variable 'p'.

Reorder the terms:
6p2 + 13p3 + 6p4 = -13p3 + 13p3

Combine like terms: -13p3 + 13p3 = 0
6p2 + 13p3 + 6p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(6 + 13p + 6p2) = 0

Factor a trinomial.
p2((3 + 2p)(2 + 3p)) = 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 '(3 + 2p)' equal to zero and attempt to solve:

Simplifying
3 + 2p = 0

Solving
3 + 2p = 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 + 2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2p = 0 + -3
2p = 0 + -3

Combine like terms: 0 + -3 = -3
2p = -3

Divide each side by '2'.
p = -1.5

Simplifying
p = -1.5
Subproblem 3
Set the factor '(2 + 3p)' equal to zero and attempt to solve:

Simplifying
2 + 3p = 0

Solving
2 + 3p = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3p = 0 + -2
3p = 0 + -2

Combine like terms: 0 + -2 = -2
3p = -2

Divide each side by '3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
Solution
p = {0, -1.5, -0.6666666667}