(3a+2b)(2a-2b)=0

Solution for (3a+2b)(2a-2b)=0 equation:

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

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

Reorder the terms:
((-6ab + 6a2) + 2b * (2a + -2b)) = 0
((-6ab + 6a2) + 2b * (2a + -2b)) = 0
(-6ab + 6a2 + (2a * 2b + -2b * 2b)) = 0
(-6ab + 6a2 + (4ab + -4b2)) = 0

Reorder the terms:
(-6ab + 4ab + 6a2 + -4b2) = 0

Combine like terms: -6ab + 4ab = -2ab
(-2ab + 6a2 + -4b2) = 0

Solving
-2ab + 6a2 + -4b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ab + 3a2 + -2b2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(a + -1b)' equal to zero and attempt to solve:

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

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

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

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

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

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

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