r^2-5rz+6z^2=

Solution for r^2-5rz+6z^2= equation:

Simplifying
r2 + -5rz + 6z2 = 0

Reorder the terms:
-5rz + r2 + 6z2 = 0

Solving
-5rz + r2 + 6z2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -3z)(r + -2z) = 0

Subproblem 1
Set the factor '(r + -3z)' equal to zero and attempt to solve:

Simplifying
r + -3z = 0

Solving
r + -3z = 0

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

Add '3z' to each side of the equation.
r + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
r + 0 = 0 + 3z
r = 0 + 3z
Remove the zero:
r = 3z

Simplifying
r = 3z
Subproblem 2
Set the factor '(r + -2z)' equal to zero and attempt to solve:

Simplifying
r + -2z = 0

Solving
r + -2z = 0

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

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

Combine like terms: -2z + 2z = 0
r + 0 = 0 + 2z
r = 0 + 2z
Remove the zero:
r = 2z

Simplifying
r = 2z
Solution
r = {3z, 2z}