4r^2-24r+11=0

Solution for 4r^2-24r+11=0 equation:

Simplifying
4r2 + -24r + 11 = 0

Reorder the terms:
11 + -24r + 4r2 = 0

Solving
11 + -24r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -2r)(11 + -2r) = 0

Subproblem 1
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(11 + -2r)' equal to zero and attempt to solve:

Simplifying
11 + -2r = 0

Solving
11 + -2r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2r = 0 + -11
-2r = 0 + -11

Combine like terms: 0 + -11 = -11
-2r = -11

Divide each side by '-2'.
r = 5.5

Simplifying
r = 5.5
Solution
r = {0.5, 5.5}