45=-4r+r^2

Solution for 45=-4r+r^2 equation:

Simplifying
45 = -4r + r2

Solving
45 = -4r + r2

Solving for variable 'r'.

Reorder the terms:
45 + 4r + -1r2 = -4r + 4r + r2 + -1r2

Combine like terms: -4r + 4r = 0
45 + 4r + -1r2 = 0 + r2 + -1r2
45 + 4r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
45 + 4r + -1r2 = 0

Factor a trinomial.
(9 + -1r)(5 + r) = 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 '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

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

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

Simplifying
r = -5
Solution
r = {9, -5}