8u^2-31u-4=0

Solution for 8u^2-31u-4=0 equation:

Simplifying
8u2 + -31u + -4 = 0

Reorder the terms:
-4 + -31u + 8u2 = 0

Solving
-4 + -31u + 8u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -8u)(4 + -1u) = 0

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

Simplifying
-1 + -8u = 0

Solving
-1 + -8u = 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 + -8u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8u = 0 + 1
-8u = 0 + 1

Combine like terms: 0 + 1 = 1
-8u = 1

Divide each side by '-8'.
u = -0.125

Simplifying
u = -0.125
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {-0.125, 4}