(y-ax)(9y+6ax)=0

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Solution for (y-ax)(9y+6ax)=0 equation: 


Simplifying
(y + -1ax)(9y + 6ax) = 0

Reorder the terms:
(-1ax + y)(9y + 6ax) = 0

Reorder the terms:
(-1ax + y)(6ax + 9y) = 0

Multiply (-1ax + y) * (6ax + 9y)
(-1ax * (6ax + 9y) + y(6ax + 9y)) = 0
((6ax * -1ax + 9y * -1ax) + y(6ax + 9y)) = 0

Reorder the terms:
((-9axy + -6a2x2) + y(6ax + 9y)) = 0
((-9axy + -6a2x2) + y(6ax + 9y)) = 0
(-9axy + -6a2x2 + (6ax * y + 9y * y)) = 0
(-9axy + -6a2x2 + (6axy + 9y2)) = 0

Reorder the terms:
(-9axy + 6axy + -6a2x2 + 9y2) = 0

Combine like terms: -9axy + 6axy = -3axy
(-3axy + -6a2x2 + 9y2) = 0

Solving
-3axy + -6a2x2 + 9y2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1axy + -2a2x2 + 3y2) = 0

Factor a trinomial.
3((-2ax + -3y)(ax + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2ax + -3y)' equal to zero and attempt to solve:

Simplifying
-2ax + -3y = 0

Solving
-2ax + -3y = 0

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

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

Combine like terms: -3y + 3y = 0
-2ax + 0 = 0 + 3y
-2ax = 0 + 3y
Remove the zero:
-2ax = 3y

Divide each side by '-2x'.
a = -1.5x-1y

Simplifying
a = -1.5x-1y

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

Simplifying
ax + -1y = 0

Solving
ax + -1y = 0

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

Add 'y' to each side of the equation.
ax + -1y + y = 0 + y

Combine like terms: -1y + y = 0
ax + 0 = 0 + y
ax = 0 + y
Remove the zero:
ax = y

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

Simplifying
a = x-1y
Solution
a = {-1.5x-1y, x-1y}

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