3u^4+12u^3+42u^2=0

Solution for 3u^4+12u^3+42u^2=0 equation:

Simplifying
3u4 + 12u3 + 42u2 = 0

Reorder the terms:
42u2 + 12u3 + 3u4 = 0

Solving
42u2 + 12u3 + 3u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3u2'.
3u2(14 + 4u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve:

Simplifying
u2 = 0

Solving
u2 = 0

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

Simplifying
u2 = 0

Take the square root of each side:
u = {0}
Subproblem 2
Set the factor '(14 + 4u + u2)' equal to zero and attempt to solve:

Simplifying
14 + 4u + u2 = 0

Solving
14 + 4u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 4u + -14 + u2 = 0 + -14

Reorder the terms:
14 + -14 + 4u + u2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 4u + u2 = 0 + -14
4u + u2 = 0 + -14

Combine like terms: 0 + -14 = -14
4u + u2 = -14

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

Add '4' to each side of the equation.
4u + 4 + u2 = -14 + 4

Reorder the terms:
4 + 4u + u2 = -14 + 4

Combine like terms: -14 + 4 = -10
4 + 4u + u2 = -10

Factor a perfect square on the left side:
(u + 2)(u + 2) = -10

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
u = {0}