r(r-1)-90=0

Solution for r(r-1)-90=0 equation:

Simplifying
r(r + -1) + -90 = 0

Reorder the terms:
r(-1 + r) + -90 = 0
(-1 * r + r * r) + -90 = 0
(-1r + r2) + -90 = 0

Reorder the terms:
-90 + -1r + r2 = 0

Solving
-90 + -1r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -1r)(10 + -1r) = 0

Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
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 = {-9, 10}