9a(ab+3)(3ab-2)=

Solution for 9a(ab+3)(3ab-2)= equation:

Simplifying
9a(ab + 3)(3ab + -2) = 0

Reorder the terms:
9a(3 + ab)(3ab + -2) = 0

Reorder the terms:
9a(3 + ab)(-2 + 3ab) = 0

Multiply (3 + ab) * (-2 + 3ab)
9a(3(-2 + 3ab) + ab(-2 + 3ab)) = 0
9a((-2 * 3 + 3ab * 3) + ab(-2 + 3ab)) = 0
9a((-6 + 9ab) + ab(-2 + 3ab)) = 0
9a(-6 + 9ab + (-2 * ab + 3ab * ab)) = 0
9a(-6 + 9ab + (-2ab + 3a2b2)) = 0

Combine like terms: 9ab + -2ab = 7ab
9a(-6 + 7ab + 3a2b2) = 0
(-6 * 9a + 7ab * 9a + 3a2b2 * 9a) = 0
(-54a + 63a2b + 27a3b2) = 0

Solving
-54a + 63a2b + 27a3b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '9a'.
9a(-6 + 7ab + 3a2b2) = 0

Factor a trinomial.
9a((-3 + -1ab)(2 + -3ab)) = 0

Ignore the factor 9.
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 '(-3 + -1ab)' equal to zero and attempt to solve:

Simplifying
-3 + -1ab = 0

Solving
-3 + -1ab = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -1ab = 0 + 3
-1ab = 0 + 3

Combine like terms: 0 + 3 = 3
-1ab = 3

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

Simplifying
a = -3b-1
Subproblem 3
Set the factor '(2 + -3ab)' equal to zero and attempt to solve:

Simplifying
2 + -3ab = 0

Solving
2 + -3ab = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3ab = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3ab = 0 + -2
-3ab = 0 + -2

Combine like terms: 0 + -2 = -2
-3ab = -2

Divide each side by '-3b'.
a = 0.6666666667b-1

Simplifying
a = 0.6666666667b-1
Solution
a = {0, -3b-1, 0.6666666667b-1}