r^2=45-4r

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

Simplifying
r2 = 45 + -4r

Solving
r2 = 45 + -4r

Solving for variable 'r'.

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

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

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

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

Factor a trinomial.
(-9 + -1r)(5 + -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 '(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
Solution
r = {-9, 5}