(r-10)(r-1)=0

Solution for (r-10)(r-1)=0 equation:

Simplifying
(r + -10)(r + -1) = 0

Reorder the terms:
(-10 + r)(r + -1) = 0

Reorder the terms:
(-10 + r)(-1 + r) = 0

Multiply (-10 + r) * (-1 + r)
(-10(-1 + r) + r(-1 + r)) = 0
((-1 * -10 + r * -10) + r(-1 + r)) = 0
((10 + -10r) + r(-1 + r)) = 0
(10 + -10r + (-1 * r + r * r)) = 0
(10 + -10r + (-1r + r2)) = 0

Combine like terms: -10r + -1r = -11r
(10 + -11r + r2) = 0

Solving
10 + -11r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -1r)(10 + -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 '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {1, 10}