4r^2+24r=64

Solution for 4r^2+24r=64 equation:

Simplifying
4r2 + 24r = 64

Reorder the terms:
24r + 4r2 = 64

Solving
24r + 4r2 = 64

Solving for variable 'r'.

Reorder the terms:
-64 + 24r + 4r2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 24r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 6r + r2) = 0

Factor a trinomial.
4((-8 + -1r)(2 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-8, 2}