r^2-r=36+4r

Solution for r^2-r=36+4r equation:

Simplifying
r2 + -1r = 36 + 4r

Reorder the terms:
-1r + r2 = 36 + 4r

Solving
-1r + r2 = 36 + 4r

Solving for variable 'r'.

Reorder the terms:
-36 + -1r + -4r + r2 = 36 + 4r + -36 + -4r

Combine like terms: -1r + -4r = -5r
-36 + -5r + r2 = 36 + 4r + -36 + -4r

Reorder the terms:
-36 + -5r + r2 = 36 + -36 + 4r + -4r

Combine like terms: 36 + -36 = 0
-36 + -5r + r2 = 0 + 4r + -4r
-36 + -5r + r2 = 4r + -4r

Combine like terms: 4r + -4r = 0
-36 + -5r + r2 = 0

Factor a trinomial.
(-4 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

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

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

Divide each side by '-1'.
r = -4

Simplifying
r = -4
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 = {-4, 9}