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

Solution for -2(u+1)(-u+3)=0 equation:

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

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

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

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

Combine like terms: -1u + 3u = 2u
-2(3 + 2u + -1u2) = 0
(3 * -2 + 2u * -2 + -1u2 * -2) = 0
(-6 + -4u + 2u2) = 0

Solving
-6 + -4u + 2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2u + u2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve:

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1u = 0 + 1

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

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

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

Simplifying
u = -1
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 = {-1, 3}