(ab-3)(ab-3)=

Solution for (ab-3)(ab-3)= equation:

Simplifying
(ab + -3)(ab + -3) = 0

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

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

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

Combine like terms: -3ab + -3ab = -6ab
(9 + -6ab + a2b2) = 0

Solving
9 + -6ab + a2b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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 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
Solution
a = {3b-1, 3b-1}