14p^4-7p^3+7p^2=0

Solution for 14p^4-7p^3+7p^2=0 equation:

Simplifying
14p4 + -7p3 + 7p2 = 0

Reorder the terms:
7p2 + -7p3 + 14p4 = 0

Solving
7p2 + -7p3 + 14p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '7p2'.
7p2(1 + -1p + 2p2) = 0

Ignore the factor 7.
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 '(1 + -1p + 2p2)' equal to zero and attempt to solve:

Simplifying
1 + -1p + 2p2 = 0

Solving
1 + -1p + 2p2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + -0.5p + p2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.5p + -0.5 + p2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.5p + p2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.5p + p2 = 0 + -0.5
-0.5p + p2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.5p + p2 = -0.5

The p term is -0.5p.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5p + 0.0625 + p2 = -0.5 + 0.0625

Reorder the terms:
0.0625 + -0.5p + p2 = -0.5 + 0.0625

Combine like terms: -0.5 + 0.0625 = -0.4375
0.0625 + -0.5p + p2 = -0.4375

Factor a perfect square on the left side:
(p + -0.25)(p + -0.25) = -0.4375

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}