(7+u)(2u+9)=0

Solution for (7+u)(2u+9)=0 equation:

Simplifying
(7 + u)(2u + 9) = 0

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

Multiply (7 + u) * (9 + 2u)
(7(9 + 2u) + u(9 + 2u)) = 0
((9 * 7 + 2u * 7) + u(9 + 2u)) = 0
((63 + 14u) + u(9 + 2u)) = 0
(63 + 14u + (9 * u + 2u * u)) = 0
(63 + 14u + (9u + 2u2)) = 0

Combine like terms: 14u + 9u = 23u
(63 + 23u + 2u2) = 0

Solving
63 + 23u + 2u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

Solving
7 + u = 0

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

Add '-7' to each side of the equation.
7 + -7 + u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + u = 0 + -7
u = 0 + -7

Combine like terms: 0 + -7 = -7
u = -7

Simplifying
u = -7
Subproblem 2
Set the factor '(9 + 2u)' equal to zero and attempt to solve:

Simplifying
9 + 2u = 0

Solving
9 + 2u = 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 + 2u = 0 + -9

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

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

Divide each side by '2'.
u = -4.5

Simplifying
u = -4.5
Solution
u = {-7, -4.5}