(r-4)(r-1)=0

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

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

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

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

Multiply (-4 + r) * (-1 + r)
(-4(-1 + r) + r(-1 + r)) = 0
((-1 * -4 + r * -4) + r(-1 + r)) = 0
((4 + -4r) + r(-1 + r)) = 0
(4 + -4r + (-1 * r + r * r)) = 0
(4 + -4r + (-1r + r2)) = 0

Combine like terms: -4r + -1r = -5r
(4 + -5r + r2) = 0

Solving
4 + -5r + r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

Divide each side by '-1'.
r = 1

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

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

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

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

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

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

Simplifying
r = 4
Solution
r = {1, 4}