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

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

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

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

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

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

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

Solving
-6 + -1u + u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1u = 0 + 2
-1u = 0 + 2

Combine like terms: 0 + 2 = 2
-1u = 2

Divide each side by '-1'.
u = -2

Simplifying
u = -2
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 = {-2, 3}