(4a-2b)*(3a+3b)=

Solution for (4a-2b)*(3a+3b)= equation:

Simplifying
(4a + -2b)(3a + 3b) = 0

Multiply (4a + -2b) * (3a + 3b)
(4a * (3a + 3b) + -2b * (3a + 3b)) = 0
((3a * 4a + 3b * 4a) + -2b * (3a + 3b)) = 0

Reorder the terms:
((12ab + 12a2) + -2b * (3a + 3b)) = 0
((12ab + 12a2) + -2b * (3a + 3b)) = 0
(12ab + 12a2 + (3a * -2b + 3b * -2b)) = 0
(12ab + 12a2 + (-6ab + -6b2)) = 0

Reorder the terms:
(12ab + -6ab + 12a2 + -6b2) = 0

Combine like terms: 12ab + -6ab = 6ab
(6ab + 12a2 + -6b2) = 0

Solving
6ab + 12a2 + -6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(ab + 2a2 + -1b2) = 0

Factor a trinomial.
6((2a + -1b)(a + b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve:

Simplifying
2a + -1b = 0

Solving
2a + -1b = 0

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

Add 'b' to each side of the equation.
2a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
2a + 0 = 0 + b
2a = 0 + b
Remove the zero:
2a = b

Divide each side by '2'.
a = 0.5b

Simplifying
a = 0.5b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {0.5b, -1b}