2x^3+2x^2y-84xy^2=0

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Solution for 2x^3+2x^2y-84xy^2=0 equation: 


Simplifying
2x3 + 2x2y + -84xy2 = 0

Reorder the terms:
-84xy2 + 2x2y + 2x3 = 0

Solving
-84xy2 + 2x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-42y2 + xy + x2) = 0

Factor a trinomial.
2x((-7y + -1x)(6y + -1x)) = 0

Ignore the factor 2.

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 '(-7y + -1x)' equal to zero and attempt to solve:

Simplifying
-7y + -1x = 0

Reorder the terms:
-1x + -7y = 0

Solving
-1x + -7y = 0

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

Add '7y' to each side of the equation.
-1x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
-1x + 0 = 0 + 7y
-1x = 0 + 7y
Remove the zero:
-1x = 7y

Divide each side by '-1'.
x = -7y

Simplifying
x = -7y

Subproblem 3
Set the factor '(6y + -1x)' equal to zero and attempt to solve:

Simplifying
6y + -1x = 0

Reorder the terms:
-1x + 6y = 0

Solving
-1x + 6y = 0

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

Add '-6y' to each side of the equation.
-1x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
-1x + 0 = 0 + -6y
-1x = 0 + -6y
Remove the zero:
-1x = -6y

Divide each side by '-1'.
x = 6y

Simplifying
x = 6y
Solution
x = {0, -7y, 6y}

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