3u^2+u-4=0

Solution for 3u^2+u-4=0 equation:

Simplifying
3u2 + u + -4 = 0

Reorder the terms:
-4 + u + 3u2 = 0

Solving
-4 + u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -3u)(1 + -1u) = 0

Subproblem 1
Set the factor '(-4 + -3u)' equal to zero and attempt to solve:

Simplifying
-4 + -3u = 0

Solving
-4 + -3u = 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 + -3u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3u = 0 + 4
-3u = 0 + 4

Combine like terms: 0 + 4 = 4
-3u = 4

Divide each side by '-3'.
u = -1.333333333

Simplifying
u = -1.333333333
Subproblem 2
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
Solution
u = {-1.333333333, 1}