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

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

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

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

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

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

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

Solving
4 + -5v + 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}