2u^2-6-u=0

Solution for 2u^2-6-u=0 equation:

Simplifying
2u2 + -6 + -1u = 0

Reorder the terms:
-6 + -1u + 2u2 = 0

Solving
-6 + -1u + 2u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-3 + -2u = 0

Solving
-3 + -2u = 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 + -2u = 0 + 3

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

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

Divide each side by '-2'.
u = -1.5

Simplifying
u = -1.5
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 = {-1.5, 2}