a^2+12ab+32b^2=0

Solution for a^2+12ab+32b^2=0 equation:

Simplifying
a2 + 12ab + 32b2 = 0

Reorder the terms:
12ab + a2 + 32b2 = 0

Solving
12ab + a2 + 32b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-4b, -8b}