(v-1)(v+5)=0

Solution for (v-1)(v+5)=0 equation:

Simplifying
(v + -1)(v + 5) = 0

Reorder the terms:
(-1 + v)(v + 5) = 0

Reorder the terms:
(-1 + v)(5 + v) = 0

Multiply (-1 + v) * (5 + v)
(-1(5 + v) + v(5 + v)) = 0
((5 * -1 + v * -1) + v(5 + v)) = 0
((-5 + -1v) + v(5 + v)) = 0
(-5 + -1v + (5 * v + v * v)) = 0
(-5 + -1v + (5v + v2)) = 0

Combine like terms: -1v + 5v = 4v
(-5 + 4v + v2) = 0

Solving
-5 + 4v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-5 + -1v)(1 + -1v) = 0

Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5
Subproblem 2
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
Solution
v = {-5, 1}