6w^2=13w-6

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

Simplifying
6w2 = 13w + -6

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

Solving
6w2 = -6 + 13w

Solving for variable 'w'.

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

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

Combine like terms: -6 + 6 = 0
6 + -13w + 6w2 = 0 + 13w + -13w
6 + -13w + 6w2 = 13w + -13w

Combine like terms: 13w + -13w = 0
6 + -13w + 6w2 = 0

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

Subproblem 1
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
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 = {0.6666666667, 1.5}