p^4-15p^2+54=0

Solution for p^4-15p^2+54=0 equation:

Simplifying
p4 + -15p2 + 54 = 0

Reorder the terms:
54 + -15p2 + p4 = 0

Solving
54 + -15p2 + p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(6 + -1p2)(9 + -1p2) = 0

Factor a difference between two squares.
(6 + -1p2)((3 + p)(3 + -1p)) = 0

Subproblem 1
Set the factor '(6 + -1p2)' equal to zero and attempt to solve:

Simplifying
6 + -1p2 = 0

Solving
6 + -1p2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p2 = 0 + -6
-1p2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1p2 = -6

Divide each side by '-1'.
p2 = 6

Simplifying
p2 = 6

Take the square root of each side:
p = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

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

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

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

Simplifying
p = -3
Subproblem 3
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

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

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

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-2.449489743, 2.449489743, -3, 3}