3x^6y^4+45x^5y^5+162x^4y^6=0

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Solution for 3x^6y^4+45x^5y^5+162x^4y^6=0 equation:


Simplifying
3x6y4 + 45x5y5 + 162x4y6 = 0

Reorder the terms:
162x4y6 + 45x5y5 + 3x6y4 = 0

Solving
162x4y6 + 45x5y5 + 3x6y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x4y4'.
3x4y4(54y2 + 15xy + x2) = 0

Factor a trinomial.
3x4y4((9y + x)(6y + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x4y4' equal to zero and attempt to solve: Simplifying x4y4 = 0 Solving x4y4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4y4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(9y + x)' equal to zero and attempt to solve: Simplifying 9y + x = 0 Reorder the terms: x + 9y = 0 Solving x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 x + 0 = 0 + -9y x = 0 + -9y Remove the zero: x = -9y Simplifying x = -9y

Subproblem 3

Set the factor '(6y + x)' equal to zero and attempt to solve: Simplifying 6y + x = 0 Reorder the terms: x + 6y = 0 Solving x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 x + 0 = 0 + -6y x = 0 + -6y Remove the zero: x = -6y Simplifying x = -6y

Solution

x = {-9y, -6y}

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