(r-5)(r-5)=100

Solution for (r-5)(r-5)=100 equation:

Simplifying
(r + -5)(r + -5) = 100

Reorder the terms:
(-5 + r)(r + -5) = 100

Reorder the terms:
(-5 + r)(-5 + r) = 100

Multiply (-5 + r) * (-5 + r)
(-5(-5 + r) + r(-5 + r)) = 100
((-5 * -5 + r * -5) + r(-5 + r)) = 100
((25 + -5r) + r(-5 + r)) = 100
(25 + -5r + (-5 * r + r * r)) = 100
(25 + -5r + (-5r + r2)) = 100

Combine like terms: -5r + -5r = -10r
(25 + -10r + r2) = 100

Solving
25 + -10r + r2 = 100

Solving for variable 'r'.

Reorder the terms:
25 + -100 + -10r + r2 = 100 + -100

Combine like terms: 25 + -100 = -75
-75 + -10r + r2 = 100 + -100

Combine like terms: 100 + -100 = 0
-75 + -10r + r2 = 0

Factor a trinomial.
(-5 + -1r)(15 + -1r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

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

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

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

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

Simplifying
r = -5
Subproblem 2
Set the factor '(15 + -1r)' equal to zero and attempt to solve:

Simplifying
15 + -1r = 0

Solving
15 + -1r = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1r = 0 + -15
-1r = 0 + -15

Combine like terms: 0 + -15 = -15
-1r = -15

Divide each side by '-1'.
r = 15

Simplifying
r = 15
Solution
r = {-5, 15}