p^4-2p^3+12p^2=0

Solution for p^4-2p^3+12p^2=0 equation:

Simplifying
p4 + -2p3 + 12p2 = 0

Reorder the terms:
12p2 + -2p3 + p4 = 0

Solving
12p2 + -2p3 + p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(12 + -2p + p2) = 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 '(12 + -2p + p2)' equal to zero and attempt to solve:

Simplifying
12 + -2p + p2 = 0

Solving
12 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -2p + -12 + p2 = 0 + -12

Reorder the terms:
12 + -12 + -2p + p2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -2p + p2 = 0 + -12
-2p + p2 = 0 + -12

Combine like terms: 0 + -12 = -12
-2p + p2 = -12

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = -12 + 1

Reorder the terms:
1 + -2p + p2 = -12 + 1

Combine like terms: -12 + 1 = -11
1 + -2p + p2 = -11

Factor a perfect square on the left side:
(p + -1)(p + -1) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}