18x^3-61x^2y-7xy^2=0

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Solution for 18x^3-61x^2y-7xy^2=0 equation: 


Simplifying
18x3 + -61x2y + -7xy2 = 0

Reorder the terms:
-7xy2 + -61x2y + 18x3 = 0

Solving
-7xy2 + -61x2y + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7y2 + -61xy + 18x2) = 0

Factor a trinomial.
x((-1y + -9x)(7y + -2x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1y + -9x)' equal to zero and attempt to solve:

Simplifying
-1y + -9x = 0

Reorder the terms:
-9x + -1y = 0

Solving
-9x + -1y = 0

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

Add 'y' to each side of the equation.
-9x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
-9x + 0 = 0 + y
-9x = 0 + y
Remove the zero:
-9x = y

Divide each side by '-9'.
x = -0.1111111111y

Simplifying
x = -0.1111111111y

Subproblem 3
Set the factor '(7y + -2x)' equal to zero and attempt to solve:

Simplifying
7y + -2x = 0

Reorder the terms:
-2x + 7y = 0

Solving
-2x + 7y = 0

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

Add '-7y' to each side of the equation.
-2x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
-2x + 0 = 0 + -7y
-2x = 0 + -7y
Remove the zero:
-2x = -7y

Divide each side by '-2'.
x = 3.5y

Simplifying
x = 3.5y
Solution
x = {0, -0.1111111111y, 3.5y}

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