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

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

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

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

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

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

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

Solving
-4ab + a2 + -32b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -8b)(a + 4b) = 0

Subproblem 1
Set the factor '(a + -8b)' equal to zero and attempt to solve:

Simplifying
a + -8b = 0

Solving
a + -8b = 0

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

Add '8b' to each side of the equation.
a + -8b + 8b = 0 + 8b

Combine like terms: -8b + 8b = 0
a + 0 = 0 + 8b
a = 0 + 8b
Remove the zero:
a = 8b

Simplifying
a = 8b
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 = {8b, -4b}