(-3a+9x)(2a-2x)=

Solution for (-3a+9x)(2a-2x)= equation:

Simplifying
(-3a + 9x)(2a + -2x) = 0

Multiply (-3a + 9x) * (2a + -2x)
(-3a * (2a + -2x) + 9x * (2a + -2x)) = 0
((2a * -3a + -2x * -3a) + 9x * (2a + -2x)) = 0

Reorder the terms:
((6ax + -6a2) + 9x * (2a + -2x)) = 0
((6ax + -6a2) + 9x * (2a + -2x)) = 0
(6ax + -6a2 + (2a * 9x + -2x * 9x)) = 0
(6ax + -6a2 + (18ax + -18x2)) = 0

Reorder the terms:
(6ax + 18ax + -6a2 + -18x2) = 0

Combine like terms: 6ax + 18ax = 24ax
(24ax + -6a2 + -18x2) = 0

Solving
24ax + -6a2 + -18x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4ax + -1a2 + -3x2) = 0

Factor a trinomial.
6((-1a + x)(a + -3x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1a + x)' equal to zero and attempt to solve:

Simplifying
-1a + x = 0

Solving
-1a + x = 0

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

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

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

Divide each side by '-1'.
a = x

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

Simplifying
a + -3x = 0

Solving
a + -3x = 0

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

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

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

Simplifying
a = 3x
Solution
a = {x, 3x}