(3-u)(2u+7)=0

Solution for (3-u)(2u+7)=0 equation:

Simplifying
(3 + -1u)(2u + 7) = 0

Reorder the terms:
(3 + -1u)(7 + 2u) = 0

Multiply (3 + -1u) * (7 + 2u)
(3(7 + 2u) + -1u * (7 + 2u)) = 0
((7 * 3 + 2u * 3) + -1u * (7 + 2u)) = 0
((21 + 6u) + -1u * (7 + 2u)) = 0
(21 + 6u + (7 * -1u + 2u * -1u)) = 0
(21 + 6u + (-7u + -2u2)) = 0

Combine like terms: 6u + -7u = -1u
(21 + -1u + -2u2) = 0

Solving
21 + -1u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + -1u)(7 + 2u) = 0

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

Simplifying
3 + -1u = 0

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

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Subproblem 2
Set the factor '(7 + 2u)' equal to zero and attempt to solve:

Simplifying
7 + 2u = 0

Solving
7 + 2u = 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 + 2u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2u = 0 + -7
2u = 0 + -7

Combine like terms: 0 + -7 = -7
2u = -7

Divide each side by '2'.
u = -3.5

Simplifying
u = -3.5
Solution
u = {3, -3.5}