4v^4-12v^3+48v^2=0

Solution for 4v^4-12v^3+48v^2=0 equation:

Simplifying
4v4 + -12v3 + 48v2 = 0

Reorder the terms:
48v2 + -12v3 + 4v4 = 0

Solving
48v2 + -12v3 + 4v4 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4v2'.
4v2(12 + -3v + v2) = 0

Ignore the factor 4.
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 '(12 + -3v + v2)' equal to zero and attempt to solve:

Simplifying
12 + -3v + v2 = 0

Solving
12 + -3v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -3v + -12 + v2 = 0 + -12

Reorder the terms:
12 + -12 + -3v + v2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -3v + v2 = 0 + -12
-3v + v2 = 0 + -12

Combine like terms: 0 + -12 = -12
-3v + v2 = -12

The v term is -3v.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3v + 2.25 + v2 = -12 + 2.25

Reorder the terms:
2.25 + -3v + v2 = -12 + 2.25

Combine like terms: -12 + 2.25 = -9.75
2.25 + -3v + v2 = -9.75

Factor a perfect square on the left side:
(v + -1.5)(v + -1.5) = -9.75

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}