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Simplifying 0 = 4x3 + 4yx2 + xy2 Reorder the terms: 0 = xy2 + 4x2y + 4x3 Solving 0 = xy2 + 4x2y + 4x3 Solving for variable 'x'. Remove the zero: -1xy2 + -4x2y + -4x3 = xy2 + 4x2y + 4x3 + -1xy2 + -4x2y + -4x3 Reorder the terms: -1xy2 + -4x2y + -4x3 = xy2 + -1xy2 + 4x2y + -4x2y + 4x3 + -4x3 Combine like terms: xy2 + -1xy2 = 0 -1xy2 + -4x2y + -4x3 = 0 + 4x2y + -4x2y + 4x3 + -4x3 -1xy2 + -4x2y + -4x3 = 4x2y + -4x2y + 4x3 + -4x3 Combine like terms: 4x2y + -4x2y = 0 -1xy2 + -4x2y + -4x3 = 0 + 4x3 + -4x3 -1xy2 + -4x2y + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -1xy2 + -4x2y + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(y2 + 4xy + 4x2) = 0 Factor a trinomial. -1x((y + 2x)(y + 2x)) = 0 Ignore the factor -1.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 = 0Subproblem 2
Set the factor '(y + 2x)' equal to zero and attempt to solve: Simplifying y + 2x = 0 Reorder the terms: 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySubproblem 3
Set the factor '(y + 2x)' equal to zero and attempt to solve: Simplifying y + 2x = 0 Reorder the terms: 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {0, -0.5y, -0.5y}
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