12u^2-4u-5=0

Solution for 12u^2-4u-5=0 equation:

Simplifying
12u2 + -4u + -5 = 0

Reorder the terms:
-5 + -4u + 12u2 = 0

Solving
-5 + -4u + 12u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -2u)(5 + -6u) = 0

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

Simplifying
-1 + -2u = 0

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

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

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

Divide each side by '-2'.
u = -0.5

Simplifying
u = -0.5
Subproblem 2
Set the factor '(5 + -6u)' equal to zero and attempt to solve:

Simplifying
5 + -6u = 0

Solving
5 + -6u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6u = 0 + -5
-6u = 0 + -5

Combine like terms: 0 + -5 = -5
-6u = -5

Divide each side by '-6'.
u = 0.8333333333

Simplifying
u = 0.8333333333
Solution
u = {-0.5, 0.8333333333}