6w^2-17w+12=0

Solution for 6w^2-17w+12=0 equation:

Simplifying
6w2 + -17w + 12 = 0

Reorder the terms:
12 + -17w + 6w2 = 0

Solving
12 + -17w + 6w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(4 + -3w)' equal to zero and attempt to solve:

Simplifying
4 + -3w = 0

Solving
4 + -3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3w = 0 + -4
-3w = 0 + -4

Combine like terms: 0 + -4 = -4
-3w = -4

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Subproblem 2
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
Solution
w = {1.333333333, 1.5}