(3t-r)(3t+r)=0

Solution for (3t-r)(3t+r)=0 equation:

Simplifying
(3t + -1r)(3t + r) = 0

Reorder the terms:
(-1r + 3t)(3t + r) = 0

Reorder the terms:
(-1r + 3t)(r + 3t) = 0

Multiply (-1r + 3t) * (r + 3t)
(-1r * (r + 3t) + 3t * (r + 3t)) = 0
((r * -1r + 3t * -1r) + 3t * (r + 3t)) = 0

Reorder the terms:
((-3rt + -1r2) + 3t * (r + 3t)) = 0
((-3rt + -1r2) + 3t * (r + 3t)) = 0
(-3rt + -1r2 + (r * 3t + 3t * 3t)) = 0
(-3rt + -1r2 + (3rt + 9t2)) = 0

Reorder the terms:
(-3rt + 3rt + -1r2 + 9t2) = 0

Combine like terms: -3rt + 3rt = 0
(0 + -1r2 + 9t2) = 0
(-1r2 + 9t2) = 0

Solving
-1r2 + 9t2 = 0

Solving for variable 'r'.

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

Add '-9t2' to each side of the equation.
-1r2 + 9t2 + -9t2 = 0 + -9t2

Combine like terms: 9t2 + -9t2 = 0
-1r2 + 0 = 0 + -9t2
-1r2 = 0 + -9t2
Remove the zero:
-1r2 = -9t2

Divide each side by '-1'.
r2 = 9t2

Simplifying
r2 = 9t2

Take the square root of each side:
r = {-3t, 3t}