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Simplifying 15x3 + 36x2y + 21y2x = 0 Reorder the terms: 21xy2 + 36x2y + 15x3 = 0 Solving 21xy2 + 36x2y + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(7y2 + 12xy + 5x2) = 0 Factor a trinomial. 3x((7y + 5x)(y + x)) = 0 Ignore the factor 3.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 + 5x)' equal to zero and attempt to solve: Simplifying 7y + 5x = 0 Reorder the terms: 5x + 7y = 0 Solving 5x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 5x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 5x + 0 = 0 + -7y 5x = 0 + -7y Remove the zero: 5x = -7y Divide each side by '5'. x = -1.4y Simplifying x = -1.4ySubproblem 3
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {0, -1.4y, -1y}
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