(r*r)+9=10r

Solution for (r*r)+9=10r equation:

Simplifying
(r * r) + 9 = 10r

Multiply r * r
(r2) + 9 = 10r
r2 + 9 = 10r

Reorder the terms:
9 + r2 = 10r

Solving
9 + r2 = 10r

Solving for variable 'r'.

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

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

Factor a trinomial.
(1 + -1r)(9 + -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 '(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
Solution
r = {1, 9}