(3x-2y)3(15x+3y)=0

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Solution for (3x-2y)3(15x+3y)=0 equation: 


Simplifying
(3x + -2y) * 3(15x + 3y) = 0

Reorder the terms for easier multiplication:
3(3x + -2y)(15x + 3y) = 0

Multiply (3x + -2y) * (15x + 3y)
3(3x * (15x + 3y) + -2y * (15x + 3y)) = 0
3((15x * 3x + 3y * 3x) + -2y * (15x + 3y)) = 0

Reorder the terms:
3((9xy + 45x2) + -2y * (15x + 3y)) = 0
3((9xy + 45x2) + -2y * (15x + 3y)) = 0
3(9xy + 45x2 + (15x * -2y + 3y * -2y)) = 0
3(9xy + 45x2 + (-30xy + -6y2)) = 0

Reorder the terms:
3(9xy + -30xy + 45x2 + -6y2) = 0

Combine like terms: 9xy + -30xy = -21xy
3(-21xy + 45x2 + -6y2) = 0
(-21xy * 3 + 45x2 * 3 + -6y2 * 3) = 0
(-63xy + 135x2 + -18y2) = 0

Solving
-63xy + 135x2 + -18y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-7xy + 15x2 + -2y2) = 0

Factor a trinomial.
9((3x + -2y)(5x + y)) = 0

Ignore the factor 9.

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

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

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

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

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve:

Simplifying
5x + y = 0

Solving
5x + y = 0

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

Add '-1y' to each side of the equation.
5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
5x + 0 = 0 + -1y
5x = 0 + -1y
Remove the zero:
5x = -1y

Divide each side by '5'.
x = -0.2y

Simplifying
x = -0.2y
Solution
x = {0.6666666667y, -0.2y}

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