(9+u)(6u+4)=0

Solution for (9+u)(6u+4)=0 equation:

Simplifying
(9 + u)(6u + 4) = 0

Reorder the terms:
(9 + u)(4 + 6u) = 0

Multiply (9 + u) * (4 + 6u)
(9(4 + 6u) + u(4 + 6u)) = 0
((4 * 9 + 6u * 9) + u(4 + 6u)) = 0
((36 + 54u) + u(4 + 6u)) = 0
(36 + 54u + (4 * u + 6u * u)) = 0
(36 + 54u + (4u + 6u2)) = 0

Combine like terms: 54u + 4u = 58u
(36 + 58u + 6u2) = 0

Solving
36 + 58u + 6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 29u + 3u2) = 0

Factor a trinomial.
2((9 + u)(2 + 3u)) = 0

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

Simplifying
9 + u = 0

Solving
9 + u = 0

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

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

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

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

Simplifying
u = -9
Subproblem 2
Set the factor '(2 + 3u)' equal to zero and attempt to solve:

Simplifying
2 + 3u = 0

Solving
2 + 3u = 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 + 3u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3u = 0 + -2
3u = 0 + -2

Combine like terms: 0 + -2 = -2
3u = -2

Divide each side by '3'.
u = -0.6666666667

Simplifying
u = -0.6666666667
Solution
u = {-9, -0.6666666667}