(2t+3r)(2t-3r)=

Solution for (2t+3r)(2t-3r)= equation:

Simplifying
(2t + 3r)(2t + -3r) = 0

Reorder the terms:
(3r + 2t)(2t + -3r) = 0

Reorder the terms:
(3r + 2t)(-3r + 2t) = 0

Multiply (3r + 2t) * (-3r + 2t)
(3r * (-3r + 2t) + 2t * (-3r + 2t)) = 0
((-3r * 3r + 2t * 3r) + 2t * (-3r + 2t)) = 0

Reorder the terms:
((6rt + -9r2) + 2t * (-3r + 2t)) = 0
((6rt + -9r2) + 2t * (-3r + 2t)) = 0
(6rt + -9r2 + (-3r * 2t + 2t * 2t)) = 0
(6rt + -9r2 + (-6rt + 4t2)) = 0

Reorder the terms:
(6rt + -6rt + -9r2 + 4t2) = 0

Combine like terms: 6rt + -6rt = 0
(0 + -9r2 + 4t2) = 0
(-9r2 + 4t2) = 0

Solving
-9r2 + 4t2 = 0

Solving for variable 'r'.

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

Add '-4t2' to each side of the equation.
-9r2 + 4t2 + -4t2 = 0 + -4t2

Combine like terms: 4t2 + -4t2 = 0
-9r2 + 0 = 0 + -4t2
-9r2 = 0 + -4t2
Remove the zero:
-9r2 = -4t2

Divide each side by '-9'.
r2 = 0.4444444444t2

Simplifying
r2 = 0.4444444444t2

Take the square root of each side:
r = {-0.666666667t, 0.666666667t}