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

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

Simplifying
(12a + -1b)(-2a + 4b) = 0

Multiply (12a + -1b) * (-2a + 4b)
(12a * (-2a + 4b) + -1b * (-2a + 4b)) = 0
((-2a * 12a + 4b * 12a) + -1b * (-2a + 4b)) = 0

Reorder the terms:
((48ab + -24a2) + -1b * (-2a + 4b)) = 0
((48ab + -24a2) + -1b * (-2a + 4b)) = 0
(48ab + -24a2 + (-2a * -1b + 4b * -1b)) = 0
(48ab + -24a2 + (2ab + -4b2)) = 0

Reorder the terms:
(48ab + 2ab + -24a2 + -4b2) = 0

Combine like terms: 48ab + 2ab = 50ab
(50ab + -24a2 + -4b2) = 0

Solving
50ab + -24a2 + -4b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25ab + -12a2 + -2b2) = 0

Factor a trinomial.
2((-12a + b)(a + -2b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12a + b)' equal to zero and attempt to solve:

Simplifying
-12a + b = 0

Solving
-12a + b = 0

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

Add '-1b' to each side of the equation.
-12a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-12a + 0 = 0 + -1b
-12a = 0 + -1b
Remove the zero:
-12a = -1b

Divide each side by '-12'.
a = 0.08333333333b

Simplifying
a = 0.08333333333b
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 = {0.08333333333b, 2b}