6x^5-7x^4y-24x^3y^2=0

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Solution for 6x^5-7x^4y-24x^3y^2=0 equation:


Simplifying
6x5 + -7x4y + -24x3y2 = 0

Reorder the terms:
-24x3y2 + -7x4y + 6x5 = 0

Solving
-24x3y2 + -7x4y + 6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-24y2 + -7xy + 6x2) = 0

Factor a trinomial.
x3((-3y + -2x)(8y + -3x)) = 0

Subproblem 1

Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(-3y + -2x)' equal to zero and attempt to solve: Simplifying -3y + -2x = 0 Reorder the terms: -2x + -3y = 0 Solving -2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. -2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 -2x + 0 = 0 + 3y -2x = 0 + 3y Remove the zero: -2x = 3y Divide each side by '-2'. x = -1.5y Simplifying x = -1.5y

Subproblem 3

Set the factor '(8y + -3x)' equal to zero and attempt to solve: Simplifying 8y + -3x = 0 Reorder the terms: -3x + 8y = 0 Solving -3x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. -3x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 -3x + 0 = 0 + -8y -3x = 0 + -8y Remove the zero: -3x = -8y Divide each side by '-3'. x = 2.666666667y Simplifying x = 2.666666667y

Solution

x = {-1.5y, 2.666666667y}

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