6w^2+38w+12=0

Solution for 6w^2+38w+12=0 equation:

Simplifying
6w2 + 38w + 12 = 0

Reorder the terms:
12 + 38w + 6w2 = 0

Solving
12 + 38w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 19w + 3w2) = 0

Factor a trinomial.
2((6 + w)(1 + 3w)) = 0

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

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(1 + 3w)' equal to zero and attempt to solve:

Simplifying
1 + 3w = 0

Solving
1 + 3w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3w = 0 + -1
3w = 0 + -1

Combine like terms: 0 + -1 = -1
3w = -1

Divide each side by '3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
Solution
w = {-6, -0.3333333333}