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Simplifying 4x3 + 35x2y + 24y2x = 0 Reorder the terms: 24xy2 + 35x2y + 4x3 = 0 Solving 24xy2 + 35x2y + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(24y2 + 35xy + 4x2) = 0 Factor a trinomial. x((8y + x)(3y + 4x)) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(8y + x)' equal to zero and attempt to solve: Simplifying 8y + x = 0 Reorder the terms: x + 8y = 0 Solving x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 x + 0 = 0 + -8y x = 0 + -8y Remove the zero: x = -8y Simplifying x = -8ySubproblem 3
Set the factor '(3y + 4x)' equal to zero and attempt to solve: Simplifying 3y + 4x = 0 Reorder the terms: 4x + 3y = 0 Solving 4x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 4x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 4x + 0 = 0 + -3y 4x = 0 + -3y Remove the zero: 4x = -3y Divide each side by '4'. x = -0.75y Simplifying x = -0.75ySolution
x = {0, -8y, -0.75y}
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