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Simplifying 2x3 + 2x2y + -84xy2 = 0 Reorder the terms: -84xy2 + 2x2y + 2x3 = 0 Solving -84xy2 + 2x2y + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-42y2 + xy + x2) = 0 Factor a trinomial. 2x((-7y + -1x)(6y + -1x)) = 0 Ignore the factor 2.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 '(-7y + -1x)' equal to zero and attempt to solve: Simplifying -7y + -1x = 0 Reorder the terms: -1x + -7y = 0 Solving -1x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. -1x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 -1x + 0 = 0 + 7y -1x = 0 + 7y Remove the zero: -1x = 7y Divide each side by '-1'. x = -7y Simplifying x = -7ySubproblem 3
Set the factor '(6y + -1x)' equal to zero and attempt to solve: Simplifying 6y + -1x = 0 Reorder the terms: -1x + 6y = 0 Solving -1x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. -1x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 -1x + 0 = 0 + -6y -1x = 0 + -6y Remove the zero: -1x = -6y Divide each side by '-1'. x = 6y Simplifying x = 6ySolution
x = {0, -7y, 6y}
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