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

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

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

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

Reorder the terms:
((6af + 9a2) + -3f * (3a + 2f)) = 0
((6af + 9a2) + -3f * (3a + 2f)) = 0
(6af + 9a2 + (3a * -3f + 2f * -3f)) = 0
(6af + 9a2 + (-9af + -6f2)) = 0

Reorder the terms:
(6af + -9af + 9a2 + -6f2) = 0

Combine like terms: 6af + -9af = -3af
(-3af + 9a2 + -6f2) = 0

Solving
-3af + 9a2 + -6f2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1af + 3a2 + -2f2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(a + -1f)' equal to zero and attempt to solve:

Simplifying
a + -1f = 0

Solving
a + -1f = 0

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

Add 'f' to each side of the equation.
a + -1f + f = 0 + f

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

Simplifying
a = f
Subproblem 2
Set the factor '(3a + 2f)' equal to zero and attempt to solve:

Simplifying
3a + 2f = 0

Solving
3a + 2f = 0

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

Add '-2f' to each side of the equation.
3a + 2f + -2f = 0 + -2f

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

Divide each side by '3'.
a = -0.6666666667f

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