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

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

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

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

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

Multiply (-2 + v) * (3 + v)
(-2(3 + v) + v(3 + v)) = 0
((3 * -2 + v * -2) + v(3 + v)) = 0
((-6 + -2v) + v(3 + v)) = 0
(-6 + -2v + (3 * v + v * v)) = 0
(-6 + -2v + (3v + v2)) = 0

Combine like terms: -2v + 3v = 1v
(-6 + 1v + v2) = 0

Solving
-6 + 1v + v2 = 0

Solving for variable 'v'.

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

Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve:

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1v = 0 + 3
-1v = 0 + 3

Combine like terms: 0 + 3 = 3
-1v = 3

Divide each side by '-1'.
v = -3

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