-6w^2+13w-6=0

Solution for -6w^2+13w-6=0 equation:

Simplifying
-6w2 + 13w + -6 = 0

Reorder the terms:
-6 + 13w + -6w2 = 0

Solving
-6 + 13w + -6w2 = 0

Solving for variable 'w'.

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

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 '(2 + -3w)' equal to zero and attempt to solve:

Simplifying
2 + -3w = 0

Solving
2 + -3w = 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 + -3w = 0 + -2

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

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

Divide each side by '-3'.
w = 0.6666666667

Simplifying
w = 0.6666666667
Solution
w = {1.5, 0.6666666667}