8p^4+9p^2=-18p^3

Solution for 8p^4+9p^2=-18p^3 equation:

Simplifying
8p4 + 9p2 = -18p3

Reorder the terms:
9p2 + 8p4 = -18p3

Solving
9p2 + 8p4 = -18p3

Solving for variable 'p'.

Reorder the terms:
9p2 + 18p3 + 8p4 = -18p3 + 18p3

Combine like terms: -18p3 + 18p3 = 0
9p2 + 18p3 + 8p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(9 + 18p + 8p2) = 0

Factor a trinomial.
p2((3 + 2p)(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 '(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 '(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, -1.5, -0.75}