a(9ab+12-13ba-4(b+4))=

Solution for a(9ab+12-13ba-4(b+4))= equation:

Simplifying
a(9ab + 12 + -13ba + -4(b + 4)) = 0

Reorder the terms:
a(9ab + 12 + -13ab + -4(4 + b)) = 0
a(9ab + 12 + -13ab + (4 * -4 + b * -4)) = 0
a(9ab + 12 + -13ab + (-16 + -4b)) = 0

Reorder the terms:
a(12 + -16 + 9ab + -13ab + -4b) = 0

Combine like terms: 12 + -16 = -4
a(-4 + 9ab + -13ab + -4b) = 0

Combine like terms: 9ab + -13ab = -4ab
a(-4 + -4ab + -4b) = 0
(-4 * a + -4ab * a + -4b * a) = 0

Reorder the terms:
(-4a + -4ab + -4a2b) = 0
(-4a + -4ab + -4a2b) = 0

Solving
-4a + -4ab + -4a2b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-4a'.
-4a(1 + b + ab) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + b + ab)' equal to zero and attempt to solve:

Simplifying
1 + b + ab = 0

Reorder the terms:
1 + ab + b = 0

Solving
1 + ab + b = 0

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

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

Reorder the terms:
1 + -1 + ab + b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + ab + b = 0 + -1
ab + b = 0 + -1

Combine like terms: 0 + -1 = -1
ab + b = -1

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

Combine like terms: b + -1b = 0
ab + 0 = -1 + -1b
ab = -1 + -1b

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

Simplifying
a = -1b-1 + -1

Reorder the terms:
a = -1 + -1b-1
Solution
a = {0, -1 + -1b-1}