9p^3-5p^2=-2p^2

Solution for 9p^3-5p^2=-2p^2 equation:

Simplifying
9p3 + -5p2 = -2p2

Reorder the terms:
-5p2 + 9p3 = -2p2

Solving
-5p2 + 9p3 = -2p2

Solving for variable 'p'.

Reorder the terms:
-5p2 + 2p2 + 9p3 = -2p2 + 2p2

Combine like terms: -5p2 + 2p2 = -3p2
-3p2 + 9p3 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
-3p2 + 9p3 = 0

Factor out the Greatest Common Factor (GCF), '3p2'.
3p2(-1 + 3p) = 0

Ignore the factor 3.
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 '(-1 + 3p)' equal to zero and attempt to solve:

Simplifying
-1 + 3p = 0

Solving
-1 + 3p = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3p = 0 + 1
3p = 0 + 1

Combine like terms: 0 + 1 = 1
3p = 1

Divide each side by '3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
Solution
p = {0, 0.3333333333}