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Simplifying 0 = 2x(3x + -5y) 0 = (3x * 2x + -5y * 2x) Reorder the terms: 0 = (-10xy + 6x2) 0 = (-10xy + 6x2) Solving 0 = -10xy + 6x2 Solving for variable 'x'. Remove the zero: 10xy + -6x2 = -10xy + 6x2 + 10xy + -6x2 Reorder the terms: 10xy + -6x2 = -10xy + 10xy + 6x2 + -6x2 Combine like terms: -10xy + 10xy = 0 10xy + -6x2 = 0 + 6x2 + -6x2 10xy + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 10xy + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(5y + -3x) = 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 '(5y + -3x)' equal to zero and attempt to solve: Simplifying 5y + -3x = 0 Reorder the terms: -3x + 5y = 0 Solving -3x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. -3x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -3x + 0 = 0 + -5y -3x = 0 + -5y Remove the zero: -3x = -5y Divide each side by '-3'. x = 1.666666667y Simplifying x = 1.666666667ySolution
x = {0, 1.666666667y}
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