6u^2-7u-3=0

Solution for 6u^2-7u-3=0 equation:

Simplifying
6u2 + -7u + -3 = 0

Reorder the terms:
-3 + -7u + 6u2 = 0

Solving
-3 + -7u + 6u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-1 + -3u = 0

Solving
-1 + -3u = 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 + -3u = 0 + 1

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

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

Divide each side by '-3'.
u = -0.3333333333

Simplifying
u = -0.3333333333
Subproblem 2
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
Solution
u = {-0.3333333333, 1.5}