3w^2=11w-6

Solution for 3w^2=11w-6 equation:

Simplifying
3w2 = 11w + -6

Reorder the terms:
3w2 = -6 + 11w

Solving
3w2 = -6 + 11w

Solving for variable 'w'.

Reorder the terms:
6 + -11w + 3w2 = -6 + 11w + 6 + -11w

Reorder the terms:
6 + -11w + 3w2 = -6 + 6 + 11w + -11w

Combine like terms: -6 + 6 = 0
6 + -11w + 3w2 = 0 + 11w + -11w
6 + -11w + 3w2 = 11w + -11w

Combine like terms: 11w + -11w = 0
6 + -11w + 3w2 = 0

Factor a trinomial.
(2 + -3w)(3 + -1w) = 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 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {0.6666666667, 3}