r^2-2rz-24z^2=0

Solution for r^2-2rz-24z^2=0 equation:

Simplifying
r2 + -2rz + -24z2 = 0

Reorder the terms:
-2rz + r2 + -24z2 = 0

Solving
-2rz + r2 + -24z2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -6z)(r + 4z) = 0

Subproblem 1
Set the factor '(r + -6z)' equal to zero and attempt to solve:

Simplifying
r + -6z = 0

Solving
r + -6z = 0

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

Add '6z' to each side of the equation.
r + -6z + 6z = 0 + 6z

Combine like terms: -6z + 6z = 0
r + 0 = 0 + 6z
r = 0 + 6z
Remove the zero:
r = 6z

Simplifying
r = 6z
Subproblem 2
Set the factor '(r + 4z)' equal to zero and attempt to solve:

Simplifying
r + 4z = 0

Solving
r + 4z = 0

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

Add '-4z' to each side of the equation.
r + 4z + -4z = 0 + -4z

Combine like terms: 4z + -4z = 0
r + 0 = 0 + -4z
r = 0 + -4z
Remove the zero:
r = -4z

Simplifying
r = -4z
Solution
r = {6z, -4z}