p^4-256=

Solution for p^4-256= equation:

Simplifying
p4 + -256 = 0

Reorder the terms:
-256 + p4 = 0

Solving
-256 + p4 = 0

Solving for variable 'p'.

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

Add '256' to each side of the equation.
-256 + 256 + p4 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + p4 = 0 + 256
p4 = 0 + 256

Combine like terms: 0 + 256 = 256
p4 = 256

Simplifying
p4 = 256

Reorder the terms:
-256 + p4 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + p4 = 0

Factor a difference between two squares.
(16 + p2)(-16 + p2) = 0

Factor a difference between two squares.
(16 + p2)((4 + p)(-4 + p)) = 0

Subproblem 1
Set the factor '(16 + p2)' equal to zero and attempt to solve:

Simplifying
16 + p2 = 0

Solving
16 + p2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + p2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + p2 = 0 + -16
p2 = 0 + -16

Combine like terms: 0 + -16 = -16
p2 = -16

Simplifying
p2 = -16

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 0

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

Add '-4' to each side of the equation.
4 + -4 + p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + p = 0 + -4
p = 0 + -4

Combine like terms: 0 + -4 = -4
p = -4

Simplifying
p = -4
Subproblem 3
Set the factor '(-4 + p)' equal to zero and attempt to solve:

Simplifying
-4 + p = 0

Solving
-4 + p = 0

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

Add '4' to each side of the equation.
-4 + 4 + p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + p = 0 + 4
p = 0 + 4

Combine like terms: 0 + 4 = 4
p = 4

Simplifying
p = 4
Solution
p = {-4, 4}