(9u+2)(6u+1)=0

Solution for (9u+2)(6u+1)=0 equation:

Simplifying
(9u + 2)(6u + 1) = 0

Reorder the terms:
(2 + 9u)(6u + 1) = 0

Reorder the terms:
(2 + 9u)(1 + 6u) = 0

Multiply (2 + 9u) * (1 + 6u)
(2(1 + 6u) + 9u * (1 + 6u)) = 0
((1 * 2 + 6u * 2) + 9u * (1 + 6u)) = 0
((2 + 12u) + 9u * (1 + 6u)) = 0
(2 + 12u + (1 * 9u + 6u * 9u)) = 0
(2 + 12u + (9u + 54u2)) = 0

Combine like terms: 12u + 9u = 21u
(2 + 21u + 54u2) = 0

Solving
2 + 21u + 54u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2 + 9u)(1 + 6u) = 0

Subproblem 1
Set the factor '(2 + 9u)' equal to zero and attempt to solve:

Simplifying
2 + 9u = 0

Solving
2 + 9u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 9u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9u = 0 + -2
9u = 0 + -2

Combine like terms: 0 + -2 = -2
9u = -2

Divide each side by '9'.
u = -0.2222222222

Simplifying
u = -0.2222222222
Subproblem 2
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
Solution
u = {-0.2222222222, -0.1666666667}