3+6(w+3)w=

Solution for 3+6(w+3)w= equation:

Simplifying
3 + 6(w + 3) * w = 0

Reorder the terms:
3 + 6(3 + w) * w = 0

Reorder the terms for easier multiplication:
3 + 6w(3 + w) = 0
3 + (3 * 6w + w * 6w) = 0
3 + (18w + 6w2) = 0

Solving
3 + 18w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 6w + 2w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 6w + 2w2)' equal to zero and attempt to solve:

Simplifying
1 + 6w + 2w2 = 0

Solving
1 + 6w + 2w2 = 0

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

Divide each side by '2'.
0.5 + 3w + w2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3w + -0.5 + w2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3w + w2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3w + w2 = 0 + -0.5
3w + w2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3w + w2 = -0.5

The w term is 3w.  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.
3w + 2.25 + w2 = -0.5 + 2.25

Reorder the terms:
2.25 + 3w + w2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + 3w + w2 = 1.75

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(w + 1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
w + 1.5 = 1.322875656

Simplifying
w + 1.5 = 1.322875656

Reorder the terms:
1.5 + w = 1.322875656

Solving
1.5 + w = 1.322875656

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 1.322875656 + -1.5
w = 1.322875656 + -1.5

Combine like terms: 1.322875656 + -1.5 = -0.177124344
w = -0.177124344

Simplifying
w = -0.177124344

Subproblem 2
w + 1.5 = -1.322875656

Simplifying
w + 1.5 = -1.322875656

Reorder the terms:
1.5 + w = -1.322875656

Solving
1.5 + w = -1.322875656

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -1.322875656 + -1.5
w = -1.322875656 + -1.5

Combine like terms: -1.322875656 + -1.5 = -2.822875656
w = -2.822875656

Simplifying
w = -2.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.177124344, -2.822875656}
Solution
w = {-0.177124344, -2.822875656}