(u-2)(u+1)=

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

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

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

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

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

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

Solving
-2 + -1u + u2 = 0

Solving for variable 'u'.

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

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 '(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 = {-1, 2}