r(r-4)=45

Solution for r(r-4)=45 equation:

Simplifying
r(r + -4) = 45

Reorder the terms:
r(-4 + r) = 45
(-4 * r + r * r) = 45
(-4r + r2) = 45

Solving
-4r + r2 = 45

Solving for variable 'r'.

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

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

Factor a trinomial.
(-5 + -1r)(9 + -1r) = 0

Subproblem 1
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
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 = {-5, 9}