4p^4-12p^2+9=0

Solution for 4p^4-12p^2+9=0 equation:

Simplifying
4p4 + -12p2 + 9 = 0

Reorder the terms:
9 + -12p2 + 4p4 = 0

Solving
9 + -12p2 + 4p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + -2p2)(3 + -2p2) = 0

Subproblem 1
Set the factor '(3 + -2p2)' equal to zero and attempt to solve:

Simplifying
3 + -2p2 = 0

Solving
3 + -2p2 = 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 + -2p2 = 0 + -3

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

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

Divide each side by '-2'.
p2 = 1.5

Simplifying
p2 = 1.5

Take the square root of each side:
p = {-1.224744871, 1.224744871}
Subproblem 2
Set the factor '(3 + -2p2)' equal to zero and attempt to solve:

Simplifying
3 + -2p2 = 0

Solving
3 + -2p2 = 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 + -2p2 = 0 + -3

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

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

Divide each side by '-2'.
p2 = 1.5

Simplifying
p2 = 1.5

Take the square root of each side:
p = {-1.224744871, 1.224744871}
Solution
p = {-1.224744871, 1.224744871, -1.224744871, 1.224744871}