16w^2+28w+6=0

Solution for 16w^2+28w+6=0 equation:

Simplifying
16w2 + 28w + 6 = 0

Reorder the terms:
6 + 28w + 16w2 = 0

Solving
6 + 28w + 16w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 14w + 8w2) = 0

Factor a trinomial.
2((3 + 2w)(1 + 4w)) = 0

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

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve:

Simplifying
1 + 4w = 0

Solving
1 + 4w = 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 + 4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4w = 0 + -1
4w = 0 + -1

Combine like terms: 0 + -1 = -1
4w = -1

Divide each side by '4'.
w = -0.25

Simplifying
w = -0.25
Solution
w = {-1.5, -0.25}