3w^2+6w+6=0

Solution for 3w^2+6w+6=0 equation:

Simplifying
3w2 + 6w + 6 = 0

Reorder the terms:
6 + 6w + 3w2 = 0

Solving
6 + 6w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 2w + w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 2w + w2)' equal to zero and attempt to solve:

Simplifying
2 + 2w + w2 = 0

Solving
2 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + 2w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2w + w2 = 0 + -2
2w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
2w + w2 = -2

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

Add '1' to each side of the equation.
2w + 1 + w2 = -2 + 1

Reorder the terms:
1 + 2w + w2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2w + w2 = -1

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

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.

The solution to this equation could not be determined.