4X^3+4X^2Y-24XY^2=0

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Solution for 4X^3+4X^2Y-24XY^2=0 equation:


Simplifying
4X3 + 4X2Y + -24XY2 = 0

Reorder the terms:
-24XY2 + 4X2Y + 4X3 = 0

Solving
-24XY2 + 4X2Y + 4X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4X'.
4X(-6Y2 + XY + X2) = 0

Factor a trinomial.
4X((-3Y + -1X)(2Y + -1X)) = 0

Ignore the factor 4.

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 '(-3Y + -1X)' equal to zero and attempt to solve: Simplifying -3Y + -1X = 0 Reorder the terms: -1X + -3Y = 0 Solving -1X + -3Y = 0 Move all terms containing X to the left, all other terms to the right. Add '3Y' to each side of the equation. -1X + -3Y + 3Y = 0 + 3Y Combine like terms: -3Y + 3Y = 0 -1X + 0 = 0 + 3Y -1X = 0 + 3Y Remove the zero: -1X = 3Y Divide each side by '-1'. X = -3Y Simplifying X = -3Y

Subproblem 3

Set the factor '(2Y + -1X)' equal to zero and attempt to solve: Simplifying 2Y + -1X = 0 Reorder the terms: -1X + 2Y = 0 Solving -1X + 2Y = 0 Move all terms containing X to the left, all other terms to the right. Add '-2Y' to each side of the equation. -1X + 2Y + -2Y = 0 + -2Y Combine like terms: 2Y + -2Y = 0 -1X + 0 = 0 + -2Y -1X = 0 + -2Y Remove the zero: -1X = -2Y Divide each side by '-1'. X = 2Y Simplifying X = 2Y

Solution

X = {0, -3Y, 2Y}

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