(3b+6ay)(b-ay)=0

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Solution for (3b+6ay)(b-ay)=0 equation: 


Simplifying
(3b + 6ay)(b + -1ay) = 0

Reorder the terms:
(6ay + 3b)(b + -1ay) = 0

Reorder the terms:
(6ay + 3b)(-1ay + b) = 0

Multiply (6ay + 3b) * (-1ay + b)
(6ay * (-1ay + b) + 3b * (-1ay + b)) = 0
((-1ay * 6ay + b * 6ay) + 3b * (-1ay + b)) = 0

Reorder the terms:
((6aby + -6a2y2) + 3b * (-1ay + b)) = 0
((6aby + -6a2y2) + 3b * (-1ay + b)) = 0
(6aby + -6a2y2 + (-1ay * 3b + b * 3b)) = 0
(6aby + -6a2y2 + (-3aby + 3b2)) = 0

Reorder the terms:
(6aby + -3aby + -6a2y2 + 3b2) = 0

Combine like terms: 6aby + -3aby = 3aby
(3aby + -6a2y2 + 3b2) = 0

Solving
3aby + -6a2y2 + 3b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(aby + -2a2y2 + b2) = 0

Factor a trinomial.
3((-2ay + -1b)(ay + -1b)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2ay + -1b)' equal to zero and attempt to solve:

Simplifying
-2ay + -1b = 0

Solving
-2ay + -1b = 0

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

Add 'b' to each side of the equation.
-2ay + -1b + b = 0 + b

Combine like terms: -1b + b = 0
-2ay + 0 = 0 + b
-2ay = 0 + b
Remove the zero:
-2ay = b

Divide each side by '-2y'.
a = -0.5by-1

Simplifying
a = -0.5by-1

Subproblem 2
Set the factor '(ay + -1b)' equal to zero and attempt to solve:

Simplifying
ay + -1b = 0

Solving
ay + -1b = 0

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

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

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

Divide each side by 'y'.
a = by-1

Simplifying
a = by-1
Solution
a = {-0.5by-1, by-1}

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