(v-4)(v+2)=0

Solution for (v-4)(v+2)=0 equation:

Simplifying
(v + -4)(v + 2) = 0

Reorder the terms:
(-4 + v)(v + 2) = 0

Reorder the terms:
(-4 + v)(2 + v) = 0

Multiply (-4 + v) * (2 + v)
(-4(2 + v) + v(2 + v)) = 0
((2 * -4 + v * -4) + v(2 + v)) = 0
((-8 + -4v) + v(2 + v)) = 0
(-8 + -4v + (2 * v + v * v)) = 0
(-8 + -4v + (2v + v2)) = 0

Combine like terms: -4v + 2v = -2v
(-8 + -2v + v2) = 0

Solving
-8 + -2v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-2 + -1v)(4 + -1v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-2, 4}