5v^4-20v^3+55v^2=0

Solution for 5v^4-20v^3+55v^2=0 equation:

Simplifying
5v4 + -20v3 + 55v2 = 0

Reorder the terms:
55v2 + -20v3 + 5v4 = 0

Solving
55v2 + -20v3 + 5v4 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5v2'.
5v2(11 + -4v + v2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}
Subproblem 2
Set the factor '(11 + -4v + v2)' equal to zero and attempt to solve:

Simplifying
11 + -4v + v2 = 0

Solving
11 + -4v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -4v + -11 + v2 = 0 + -11

Reorder the terms:
11 + -11 + -4v + v2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4v + v2 = 0 + -11
-4v + v2 = 0 + -11

Combine like terms: 0 + -11 = -11
-4v + v2 = -11

The v term is -4v.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4v + 4 + v2 = -11 + 4

Reorder the terms:
4 + -4v + v2 = -11 + 4

Combine like terms: -11 + 4 = -7
4 + -4v + v2 = -7

Factor a perfect square on the left side:
(v + -2)(v + -2) = -7

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
v = {0}