4p^4+9p^2=12p^3

Solution for 4p^4+9p^2=12p^3 equation:

Simplifying
4p4 + 9p2 = 12p3

Reorder the terms:
9p2 + 4p4 = 12p3

Solving
9p2 + 4p4 = 12p3

Solving for variable 'p'.

Reorder the terms:
9p2 + -12p3 + 4p4 = 12p3 + -12p3

Combine like terms: 12p3 + -12p3 = 0
9p2 + -12p3 + 4p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(9 + -12p + 4p2) = 0

Factor a trinomial.
p2((3 + -2p)(3 + -2p)) = 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 + -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
Solution
p = {0, 1.5, 1.5}