ab(a-4b)(a+3b)=0

Solution for ab(a-4b)(a+3b)=0 equation:

Simplifying
ab(a + -4b)(a + 3b) = 0

Multiply (a + -4b) * (a + 3b)
ab(a(a + 3b) + -4b * (a + 3b)) = 0
ab((a * a + 3b * a) + -4b * (a + 3b)) = 0

Reorder the terms:
ab((3ab + a2) + -4b * (a + 3b)) = 0
ab((3ab + a2) + -4b * (a + 3b)) = 0
ab(3ab + a2 + (a * -4b + 3b * -4b)) = 0
ab(3ab + a2 + (-4ab + -12b2)) = 0

Reorder the terms:
ab(3ab + -4ab + a2 + -12b2) = 0

Combine like terms: 3ab + -4ab = -1ab
ab(-1ab + a2 + -12b2) = 0
(-1ab * ab + a2 * ab + -12b2 * ab) = 0

Reorder the terms:
(-12ab3 + -1a2b2 + a3b) = 0
(-12ab3 + -1a2b2 + a3b) = 0

Solving
-12ab3 + -1a2b2 + a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(-12b2 + -1ab + a2) = 0

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

Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve:

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3b + -1a)' equal to zero and attempt to solve:

Simplifying
-3b + -1a = 0

Reorder the terms:
-1a + -3b = 0

Solving
-1a + -3b = 0

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

Add '3b' to each side of the equation.
-1a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
-1a + 0 = 0 + 3b
-1a = 0 + 3b
Remove the zero:
-1a = 3b

Divide each side by '-1'.
a = -3b

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

Simplifying
4b + -1a = 0

Reorder the terms:
-1a + 4b = 0

Solving
-1a + 4b = 0

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

Add '-4b' to each side of the equation.
-1a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-1a + 0 = 0 + -4b
-1a = 0 + -4b
Remove the zero:
-1a = -4b

Divide each side by '-1'.
a = 4b

Simplifying
a = 4b
Solution
a = {-3b, 4b}