(12a-3b)*(-2a+4b)=

Solution for (12a-3b)*(-2a+4b)= equation:

Simplifying
(12a + -3b)(-2a + 4b) = 0

Multiply (12a + -3b) * (-2a + 4b)
(12a * (-2a + 4b) + -3b * (-2a + 4b)) = 0
((-2a * 12a + 4b * 12a) + -3b * (-2a + 4b)) = 0

Reorder the terms:
((48ab + -24a2) + -3b * (-2a + 4b)) = 0
((48ab + -24a2) + -3b * (-2a + 4b)) = 0
(48ab + -24a2 + (-2a * -3b + 4b * -3b)) = 0
(48ab + -24a2 + (6ab + -12b2)) = 0

Reorder the terms:
(48ab + 6ab + -24a2 + -12b2) = 0

Combine like terms: 48ab + 6ab = 54ab
(54ab + -24a2 + -12b2) = 0

Solving
54ab + -24a2 + -12b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9ab + -4a2 + -2b2) = 0

Factor a trinomial.
6((-4a + b)(a + -2b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4a + b)' equal to zero and attempt to solve:

Simplifying
-4a + b = 0

Solving
-4a + b = 0

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

Add '-1b' to each side of the equation.
-4a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-4a + 0 = 0 + -1b
-4a = 0 + -1b
Remove the zero:
-4a = -1b

Divide each side by '-4'.
a = 0.25b

Simplifying
a = 0.25b
Subproblem 2
Set the factor '(a + -2b)' equal to zero and attempt to solve:

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

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

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

Simplifying
a = 2b
Solution
a = {0.25b, 2b}