(2a+8b)(4a-2b)=0

Solution for (2a+8b)(4a-2b)=0 equation:

Simplifying
(2a + 8b)(4a + -2b) = 0

Multiply (2a + 8b) * (4a + -2b)
(2a * (4a + -2b) + 8b * (4a + -2b)) = 0
((4a * 2a + -2b * 2a) + 8b * (4a + -2b)) = 0

Reorder the terms:
((-4ab + 8a2) + 8b * (4a + -2b)) = 0
((-4ab + 8a2) + 8b * (4a + -2b)) = 0
(-4ab + 8a2 + (4a * 8b + -2b * 8b)) = 0
(-4ab + 8a2 + (32ab + -16b2)) = 0

Reorder the terms:
(-4ab + 32ab + 8a2 + -16b2) = 0

Combine like terms: -4ab + 32ab = 28ab
(28ab + 8a2 + -16b2) = 0

Solving
28ab + 8a2 + -16b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7ab + 2a2 + -4b2) = 0

Factor a trinomial.
4((2a + -1b)(a + 4b)) = 0

Ignore the factor 4.
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 + 4b)' equal to zero and attempt to solve:

Simplifying
a + 4b = 0

Solving
a + 4b = 0

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

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

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

Simplifying
a = -4b
Solution
a = {0.5b, -4b}