(v-4)(v+1)=0

Solution for (v-4)(v+1)=0 equation:

Simplifying
(v + -4)(v + 1) = 0

Reorder the terms:
(-4 + v)(v + 1) = 0

Reorder the terms:
(-4 + v)(1 + v) = 0

Multiply (-4 + v) * (1 + v)
(-4(1 + v) + v(1 + v)) = 0
((1 * -4 + v * -4) + v(1 + v)) = 0
((-4 + -4v) + v(1 + v)) = 0
(-4 + -4v + (1 * v + v * v)) = 0
(-4 + -4v + (1v + v2)) = 0

Combine like terms: -4v + 1v = -3v
(-4 + -3v + v2) = 0

Solving
-4 + -3v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + -1v)(4 + -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 '(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 = {-1, 4}