p^4+9p^2-10=0

Solution for p^4+9p^2-10=0 equation:

Simplifying
p4 + 9p2 + -10 = 0

Reorder the terms:
-10 + 9p2 + p4 = 0

Solving
-10 + 9p2 + p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(-10 + -1p2)(1 + -1p2) = 0

Factor a difference between two squares.
(-10 + -1p2)((1 + p)(1 + -1p)) = 0

Subproblem 1
Set the factor '(-10 + -1p2)' equal to zero and attempt to solve:

Simplifying
-10 + -1p2 = 0

Solving
-10 + -1p2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1p2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1p2 = 0 + 10
-1p2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1p2 = 10

Divide each side by '-1'.
p2 = -10

Simplifying
p2 = -10

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 '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

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

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

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

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

Simplifying
1 + -1p = 0

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

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

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

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

Simplifying
p = 1
Solution
p = {-1, 1}