(r-1)(r-1)-36=0

Solution for (r-1)(r-1)-36=0 equation:

Simplifying
(r + -1)(r + -1) + -36 = 0

Reorder the terms:
(-1 + r)(r + -1) + -36 = 0

Reorder the terms:
(-1 + r)(-1 + r) + -36 = 0

Multiply (-1 + r) * (-1 + r)
(-1(-1 + r) + r(-1 + r)) + -36 = 0
((-1 * -1 + r * -1) + r(-1 + r)) + -36 = 0
((1 + -1r) + r(-1 + r)) + -36 = 0
(1 + -1r + (-1 * r + r * r)) + -36 = 0
(1 + -1r + (-1r + r2)) + -36 = 0

Combine like terms: -1r + -1r = -2r
(1 + -2r + r2) + -36 = 0

Reorder the terms:
1 + -36 + -2r + r2 = 0

Combine like terms: 1 + -36 = -35
-35 + -2r + r2 = 0

Solving
-35 + -2r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r)(7 + -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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-5, 7}