(v-2)(v+1)=0

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

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

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

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

Multiply (-2 + v) * (1 + v)
(-2(1 + v) + v(1 + v)) = 0
((1 * -2 + v * -2) + v(1 + v)) = 0
((-2 + -2v) + v(1 + v)) = 0
(-2 + -2v + (1 * v + v * v)) = 0
(-2 + -2v + (1v + v2)) = 0

Combine like terms: -2v + 1v = -1v
(-2 + -1v + v2) = 0

Solving
-2 + -1v + v2 = 0

Solving for variable 'v'.

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

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 0

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

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

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

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

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

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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

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

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

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

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

Simplifying
v = 2
Solution
v = {-1, 2}