4u^2=11u-6

Solution for 4u^2=11u-6 equation:

Simplifying
4u2 = 11u + -6

Reorder the terms:
4u2 = -6 + 11u

Solving
4u2 = -6 + 11u

Solving for variable 'u'.

Reorder the terms:
6 + -11u + 4u2 = -6 + 11u + 6 + -11u

Reorder the terms:
6 + -11u + 4u2 = -6 + 6 + 11u + -11u

Combine like terms: -6 + 6 = 0
6 + -11u + 4u2 = 0 + 11u + -11u
6 + -11u + 4u2 = 11u + -11u

Combine like terms: 11u + -11u = 0
6 + -11u + 4u2 = 0

Factor a trinomial.
(3 + -4u)(2 + -1u) = 0

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

Simplifying
3 + -4u = 0

Solving
3 + -4u = 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 + -4u = 0 + -3

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

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

Divide each side by '-4'.
u = 0.75

Simplifying
u = 0.75
Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {0.75, 2}