(7-u)(5u+3)=0

Solution for (7-u)(5u+3)=0 equation:

Simplifying
(7 + -1u)(5u + 3) = 0

Reorder the terms:
(7 + -1u)(3 + 5u) = 0

Multiply (7 + -1u) * (3 + 5u)
(7(3 + 5u) + -1u * (3 + 5u)) = 0
((3 * 7 + 5u * 7) + -1u * (3 + 5u)) = 0
((21 + 35u) + -1u * (3 + 5u)) = 0
(21 + 35u + (3 * -1u + 5u * -1u)) = 0
(21 + 35u + (-3u + -5u2)) = 0

Combine like terms: 35u + -3u = 32u
(21 + 32u + -5u2) = 0

Solving
21 + 32u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(7 + -1u)(3 + 5u) = 0

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

Simplifying
7 + -1u = 0

Solving
7 + -1u = 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 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Subproblem 2
Set the factor '(3 + 5u)' equal to zero and attempt to solve:

Simplifying
3 + 5u = 0

Solving
3 + 5u = 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 + 5u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5u = 0 + -3
5u = 0 + -3

Combine like terms: 0 + -3 = -3
5u = -3

Divide each side by '5'.
u = -0.6

Simplifying
u = -0.6
Solution
u = {7, -0.6}