(3u+4)(3-u)=0

Solution for (3u+4)(3-u)=0 equation:

Simplifying
(3u + 4)(3 + -1u) = 0

Reorder the terms:
(4 + 3u)(3 + -1u) = 0

Multiply (4 + 3u) * (3 + -1u)
(4(3 + -1u) + 3u * (3 + -1u)) = 0
((3 * 4 + -1u * 4) + 3u * (3 + -1u)) = 0
((12 + -4u) + 3u * (3 + -1u)) = 0
(12 + -4u + (3 * 3u + -1u * 3u)) = 0
(12 + -4u + (9u + -3u2)) = 0

Combine like terms: -4u + 9u = 5u
(12 + 5u + -3u2) = 0

Solving
12 + 5u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + -1u)(4 + 3u) = 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 '(4 + 3u)' equal to zero and attempt to solve:

Simplifying
4 + 3u = 0

Solving
4 + 3u = 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 + 3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3u = 0 + -4
3u = 0 + -4

Combine like terms: 0 + -4 = -4
3u = -4

Divide each side by '3'.
u = -1.333333333

Simplifying
u = -1.333333333
Solution
u = {3, -1.333333333}