4p^4-25p^2=-16p^2

Solution for 4p^4-25p^2=-16p^2 equation:

Simplifying
4p4 + -25p2 = -16p2

Reorder the terms:
-25p2 + 4p4 = -16p2

Solving
-25p2 + 4p4 = -16p2

Solving for variable 'p'.

Reorder the terms:
-25p2 + 16p2 + 4p4 = -16p2 + 16p2

Combine like terms: -25p2 + 16p2 = -9p2
-9p2 + 4p4 = -16p2 + 16p2

Combine like terms: -16p2 + 16p2 = 0
-9p2 + 4p4 = 0

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(-9 + 4p2) = 0

Factor a difference between two squares.
p2((3 + 2p)(-3 + 2p)) = 0

Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

Take the square root of each side:
p = {0}
Subproblem 2
Set the factor '(3 + 2p)' equal to zero and attempt to solve:

Simplifying
3 + 2p = 0

Solving
3 + 2p = 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 + 2p = 0 + -3

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

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

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

Simplifying
p = -1.5
Subproblem 3
Set the factor '(-3 + 2p)' equal to zero and attempt to solve:

Simplifying
-3 + 2p = 0

Solving
-3 + 2p = 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 + 2p = 0 + 3

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

Combine like terms: 0 + 3 = 3
2p = 3

Divide each side by '2'.
p = 1.5

Simplifying
p = 1.5
Solution
p = {0, -1.5, 1.5}