p^4+40-14p^2=0

Solution for p^4+40-14p^2=0 equation:

Simplifying
p4 + 40 + -14p2 = 0

Reorder the terms:
40 + -14p2 + p4 = 0

Solving
40 + -14p2 + p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(4 + -1p2)(10 + -1p2) = 0

Factor a difference between two squares.
((2 + p)(2 + -1p))(10 + -1p2) = 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

Take the square root of each side:
p = {-3.16227766, 3.16227766}
Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

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

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-3.16227766, 3.16227766, -2, 2}