6w^2+4w-32=0

Solution for 6w^2+4w-32=0 equation:

Simplifying
6w2 + 4w + -32 = 0

Reorder the terms:
-32 + 4w + 6w2 = 0

Solving
-32 + 4w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 2w + 3w2) = 0

Factor a trinomial.
2((-8 + -3w)(2 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -3w)' equal to zero and attempt to solve:

Simplifying
-8 + -3w = 0

Solving
-8 + -3w = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3w = 0 + 8
-3w = 0 + 8

Combine like terms: 0 + 8 = 8
-3w = 8

Divide each side by '-3'.
w = -2.666666667

Simplifying
w = -2.666666667
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-2.666666667, 2}