24r+r(r+2)=

Solution for 24r+r(r+2)= equation:

Simplifying
24r + r(r + 2) = 0

Reorder the terms:
24r + r(2 + r) = 0
24r + (2 * r + r * r) = 0
24r + (2r + r2) = 0

Combine like terms: 24r + 2r = 26r
26r + r2 = 0

Solving
26r + r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(26 + r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(26 + r)' equal to zero and attempt to solve:

Simplifying
26 + r = 0

Solving
26 + r = 0

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

Add '-26' to each side of the equation.
26 + -26 + r = 0 + -26

Combine like terms: 26 + -26 = 0
0 + r = 0 + -26
r = 0 + -26

Combine like terms: 0 + -26 = -26
r = -26

Simplifying
r = -26
Solution
r = {0, -26}