3u^2=11u-6

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

Simplifying
3u2 = 11u + -6

Reorder the terms:
3u2 = -6 + 11u

Solving
3u2 = -6 + 11u

Solving for variable 'u'.

Reorder the terms:
6 + -11u + 3u2 = -6 + 11u + 6 + -11u

Reorder the terms:
6 + -11u + 3u2 = -6 + 6 + 11u + -11u

Combine like terms: -6 + 6 = 0
6 + -11u + 3u2 = 0 + 11u + -11u
6 + -11u + 3u2 = 11u + -11u

Combine like terms: 11u + -11u = 0
6 + -11u + 3u2 = 0

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

Subproblem 1
Set the factor '(2 + -3u)' equal to zero and attempt to solve:

Simplifying
2 + -3u = 0

Solving
2 + -3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3u = 0 + -2

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

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

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

Simplifying
u = 0.6666666667
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

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

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

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

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