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

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

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

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

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

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

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

Solving
-1 + -3u + 18u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-1 + -6u = 0

Solving
-1 + -6u = 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 + -6u = 0 + 1

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

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

Divide each side by '-6'.
u = -0.1666666667

Simplifying
u = -0.1666666667
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 = {-0.1666666667, 0.3333333333}