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

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

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

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

Reorder the terms:
((6at + 9a2) + -3t * (3a + 2t)) = 0
((6at + 9a2) + -3t * (3a + 2t)) = 0
(6at + 9a2 + (3a * -3t + 2t * -3t)) = 0
(6at + 9a2 + (-9at + -6t2)) = 0

Reorder the terms:
(6at + -9at + 9a2 + -6t2) = 0

Combine like terms: 6at + -9at = -3at
(-3at + 9a2 + -6t2) = 0

Solving
-3at + 9a2 + -6t2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1at + 3a2 + -2t2) = 0

Factor a trinomial.
3((a + -1t)(3a + 2t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(a + -1t)' equal to zero and attempt to solve:

Simplifying
a + -1t = 0

Solving
a + -1t = 0

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

Add 't' to each side of the equation.
a + -1t + t = 0 + t

Combine like terms: -1t + t = 0
a + 0 = 0 + t
a = 0 + t
Remove the zero:
a = t

Simplifying
a = t
Subproblem 2
Set the factor '(3a + 2t)' equal to zero and attempt to solve:

Simplifying
3a + 2t = 0

Solving
3a + 2t = 0

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

Add '-2t' to each side of the equation.
3a + 2t + -2t = 0 + -2t

Combine like terms: 2t + -2t = 0
3a + 0 = 0 + -2t
3a = 0 + -2t
Remove the zero:
3a = -2t

Divide each side by '3'.
a = -0.6666666667t

Simplifying
a = -0.6666666667t
Solution
a = {t, -0.6666666667t}