3r^2-21r=-36

Solution for 3r^2-21r=-36 equation:

Simplifying
3r2 + -21r = -36

Reorder the terms:
-21r + 3r2 = -36

Solving
-21r + 3r2 = -36

Solving for variable 'r'.

Reorder the terms:
36 + -21r + 3r2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -21r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -7r + r2) = 0

Factor a trinomial.
3((3 + -1r)(4 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
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
Solution
r = {3, 4}