(u-2)(u+3)=

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

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

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

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

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

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

Solving
-6 + 1u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(2 + -1u) = 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 '(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
Solution
u = {-3, 2}