(2u+6)(9u+4)=0

Solution for (2u+6)(9u+4)=0 equation:

Simplifying
(2u + 6)(9u + 4) = 0

Reorder the terms:
(6 + 2u)(9u + 4) = 0

Reorder the terms:
(6 + 2u)(4 + 9u) = 0

Multiply (6 + 2u) * (4 + 9u)
(6(4 + 9u) + 2u * (4 + 9u)) = 0
((4 * 6 + 9u * 6) + 2u * (4 + 9u)) = 0
((24 + 54u) + 2u * (4 + 9u)) = 0
(24 + 54u + (4 * 2u + 9u * 2u)) = 0
(24 + 54u + (8u + 18u2)) = 0

Combine like terms: 54u + 8u = 62u
(24 + 62u + 18u2) = 0

Solving
24 + 62u + 18u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 31u + 9u2) = 0

Factor a trinomial.
2((3 + u)(4 + 9u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

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

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

Simplifying
u = -3
Subproblem 2
Set the factor '(4 + 9u)' equal to zero and attempt to solve:

Simplifying
4 + 9u = 0

Solving
4 + 9u = 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 + 9u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9u = 0 + -4
9u = 0 + -4

Combine like terms: 0 + -4 = -4
9u = -4

Divide each side by '9'.
u = -0.4444444444

Simplifying
u = -0.4444444444
Solution
u = {-3, -0.4444444444}