6w^2-34w=12

Solution for 6w^2-34w=12 equation:

Simplifying
6w2 + -34w = 12

Reorder the terms:
-34w + 6w2 = 12

Solving
-34w + 6w2 = 12

Solving for variable 'w'.

Reorder the terms:
-12 + -34w + 6w2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -34w + 6w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -17w + 3w2) = 0

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

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

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

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