(3a-6b)(2a+4b)=0

Solution for (3a-6b)(2a+4b)=0 equation:

Simplifying
(3a + -6b)(2a + 4b) = 0

Multiply (3a + -6b) * (2a + 4b)
(3a * (2a + 4b) + -6b * (2a + 4b)) = 0
((2a * 3a + 4b * 3a) + -6b * (2a + 4b)) = 0

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

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

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

Solving
6a2 + -24b2 = 0

Solving for variable 'a'.

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

Add '24b2' to each side of the equation.
6a2 + -24b2 + 24b2 = 0 + 24b2

Combine like terms: -24b2 + 24b2 = 0
6a2 + 0 = 0 + 24b2
6a2 = 0 + 24b2
Remove the zero:
6a2 = 24b2

Divide each side by '6'.
a2 = 4b2

Simplifying
a2 = 4b2

Take the square root of each side:
a = {-2b, 2b}