(2a+8b)(6a-8b)=

Solution for (2a+8b)(6a-8b)= equation:

Simplifying
(2a + 8b)(6a + -8b) = 0

Multiply (2a + 8b) * (6a + -8b)
(2a * (6a + -8b) + 8b * (6a + -8b)) = 0
((6a * 2a + -8b * 2a) + 8b * (6a + -8b)) = 0

Reorder the terms:
((-16ab + 12a2) + 8b * (6a + -8b)) = 0
((-16ab + 12a2) + 8b * (6a + -8b)) = 0
(-16ab + 12a2 + (6a * 8b + -8b * 8b)) = 0
(-16ab + 12a2 + (48ab + -64b2)) = 0

Reorder the terms:
(-16ab + 48ab + 12a2 + -64b2) = 0

Combine like terms: -16ab + 48ab = 32ab
(32ab + 12a2 + -64b2) = 0

Solving
32ab + 12a2 + -64b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8ab + 3a2 + -16b2) = 0

Factor a trinomial.
4((3a + -4b)(a + 4b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b
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 = {1.333333333b, -4b}