4r^2-24r+36=0

Solution for 4r^2-24r+36=0 equation:

Simplifying
4r2 + -24r + 36 = 0

Reorder the terms:
36 + -24r + 4r2 = 0

Solving
36 + -24r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6r + r2) = 0

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

Ignore the factor 4.
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 '(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
Solution
r = {3, 3}