9x^4+60x^3y-21x^2y^2=0

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Solution for 9x^4+60x^3y-21x^2y^2=0 equation:


Simplifying
9x4 + 60x3y + -21x2y2 = 0

Reorder the terms:
-21x2y2 + 60x3y + 9x4 = 0

Solving
-21x2y2 + 60x3y + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-7y2 + 20xy + 3x2) = 0

Factor a trinomial.
3x2((-7y + -1x)(y + -3x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: 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 '(y + -3x)' equal to zero and attempt to solve: Simplifying y + -3x = 0 Reorder the terms: -3x + y = 0 Solving -3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -3x + 0 = 0 + -1y -3x = 0 + -1y Remove the zero: -3x = -1y Divide each side by '-3'. x = 0.3333333333y Simplifying x = 0.3333333333y

Solution

x = {0, -7y, 0.3333333333y}

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