(6+u)(3u-1)=0

Solution for (6+u)(3u-1)=0 equation:

Simplifying
(6 + u)(3u + -1) = 0

Reorder the terms:
(6 + u)(-1 + 3u) = 0

Multiply (6 + u) * (-1 + 3u)
(6(-1 + 3u) + u(-1 + 3u)) = 0
((-1 * 6 + 3u * 6) + u(-1 + 3u)) = 0
((-6 + 18u) + u(-1 + 3u)) = 0
(-6 + 18u + (-1 * u + 3u * u)) = 0
(-6 + 18u + (-1u + 3u2)) = 0

Combine like terms: 18u + -1u = 17u
(-6 + 17u + 3u2) = 0

Solving
-6 + 17u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(1 + -3u) = 0

Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6
Subproblem 2
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
Solution
u = {-6, 0.3333333333}