3u^2-5u-2=6

Solution for 3u^2-5u-2=6 equation:

Simplifying
3u2 + -5u + -2 = 6

Reorder the terms:
-2 + -5u + 3u2 = 6

Solving
-2 + -5u + 3u2 = 6

Solving for variable 'u'.

Reorder the terms:
-2 + -6 + -5u + 3u2 = 6 + -6

Combine like terms: -2 + -6 = -8
-8 + -5u + 3u2 = 6 + -6

Combine like terms: 6 + -6 = 0
-8 + -5u + 3u2 = 0

Factor a trinomial.
(-1 + -1u)(8 + -3u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(8 + -3u)' equal to zero and attempt to solve:

Simplifying
8 + -3u = 0

Solving
8 + -3u = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3u = 0 + -8
-3u = 0 + -8

Combine like terms: 0 + -8 = -8
-3u = -8

Divide each side by '-3'.
u = 2.666666667

Simplifying
u = 2.666666667
Solution
u = {-1, 2.666666667}