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Simplifying 6x4 + 27x3y + -15x2y2 = 0 Reorder the terms: -15x2y2 + 27x3y + 6x4 = 0 Solving -15x2y2 + 27x3y + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-5y2 + 9xy + 2x2) = 0 Factor a trinomial. 3x2((-5y + -1x)(y + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-5y + -1x)' equal to zero and attempt to solve: Simplifying -5y + -1x = 0 Reorder the terms: -1x + -5y = 0 Solving -1x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. -1x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 -1x + 0 = 0 + 5y -1x = 0 + 5y Remove the zero: -1x = 5y Divide each side by '-1'. x = -5y Simplifying x = -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, -5y, 0.5y}
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