4a^2+8ab-12b^2=0

Solution for 4a^2+8ab-12b^2=0 equation:

Simplifying
4a2 + 8ab + -12b2 = 0

Reorder the terms:
8ab + 4a2 + -12b2 = 0

Solving
8ab + 4a2 + -12b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2ab + a2 + -3b2) = 0

Factor a trinomial.
4((a + -1b)(a + 3b)) = 0

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Subproblem 2
Set the factor '(a + 3b)' equal to zero and attempt to solve:

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {b, -3b}