r^2-24r=-144

Solution for r^2-24r=-144 equation:

Simplifying
r2 + -24r = -144

Reorder the terms:
-24r + r2 = -144

Solving
-24r + r2 = -144

Solving for variable 'r'.

Reorder the terms:
144 + -24r + r2 = -144 + 144

Combine like terms: -144 + 144 = 0
144 + -24r + r2 = 0

Factor a trinomial.
(12 + -1r)(12 + -1r) = 0

Subproblem 1
Set the factor '(12 + -1r)' equal to zero and attempt to solve:

Simplifying
12 + -1r = 0

Solving
12 + -1r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1r = 0 + -12
-1r = 0 + -12

Combine like terms: 0 + -12 = -12
-1r = -12

Divide each side by '-1'.
r = 12

Simplifying
r = 12
Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve:

Simplifying
12 + -1r = 0

Solving
12 + -1r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1r = 0 + -12
-1r = 0 + -12

Combine like terms: 0 + -12 = -12
-1r = -12

Divide each side by '-1'.
r = 12

Simplifying
r = 12
Solution
r = {12, 12}