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Simplifying 196x2y + 80x3 + 120y2x = 0 Reorder the terms: 120xy2 + 196x2y + 80x3 = 0 Solving 120xy2 + 196x2y + 80x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(30y2 + 49xy + 20x2) = 0 Factor a trinomial. 4x((5y + 4x)(6y + 5x)) = 0 Ignore the factor 4.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 '(5y + 4x)' equal to zero and attempt to solve: Simplifying 5y + 4x = 0 Reorder the terms: 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySubproblem 3
Set the factor '(6y + 5x)' equal to zero and attempt to solve: Simplifying 6y + 5x = 0 Reorder the terms: 5x + 6y = 0 Solving 5x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. 5x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 5x + 0 = 0 + -6y 5x = 0 + -6y Remove the zero: 5x = -6y Divide each side by '5'. x = -1.2y Simplifying x = -1.2ySolution
x = {0, -1.25y, -1.2y}
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