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

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

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

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

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

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

Combine like terms: -4u + 3u = -1u
-3(12 + -1u + -1u2) = 0
(12 * -3 + -1u * -3 + -1u2 * -3) = 0
(-36 + 3u + 3u2) = 0

Solving
-36 + 3u + 3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + u + u2) = 0

Factor a trinomial.
3((-4 + -1u)(3 + -1u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1u)' equal to zero and attempt to solve:

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 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 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4
Subproblem 2
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
Solution
u = {-4, 3}