10=r(r-9)

Solution for 10=r(r-9) equation:

Simplifying
10 = r(r + -9)

Reorder the terms:
10 = r(-9 + r)
10 = (-9 * r + r * r)
10 = (-9r + r2)

Solving
10 = -9r + r2

Solving for variable 'r'.

Reorder the terms:
10 + 9r + -1r2 = -9r + 9r + r2 + -1r2

Combine like terms: -9r + 9r = 0
10 + 9r + -1r2 = 0 + r2 + -1r2
10 + 9r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
10 + 9r + -1r2 = 0

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

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

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

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