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Simplifying (2x + -4y)(-1x + 5y) = 0 Multiply (2x + -4y) * (-1x + 5y) (2x * (-1x + 5y) + -4y * (-1x + 5y)) = 0 ((-1x * 2x + 5y * 2x) + -4y * (-1x + 5y)) = 0 Reorder the terms: ((10xy + -2x2) + -4y * (-1x + 5y)) = 0 ((10xy + -2x2) + -4y * (-1x + 5y)) = 0 (10xy + -2x2 + (-1x * -4y + 5y * -4y)) = 0 (10xy + -2x2 + (4xy + -20y2)) = 0 Reorder the terms: (10xy + 4xy + -2x2 + -20y2) = 0 Combine like terms: 10xy + 4xy = 14xy (14xy + -2x2 + -20y2) = 0 Solving 14xy + -2x2 + -20y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7xy + -1x2 + -10y2) = 0 Factor a trinomial. 2((-1x + 2y)(x + -5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1x + 2y)' equal to zero and attempt to solve: Simplifying -1x + 2y = 0 Solving -1x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -1x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -1x + 0 = 0 + -2y -1x = 0 + -2y Remove the zero: -1x = -2y Divide each side by '-1'. x = 2y Simplifying x = 2ySubproblem 2
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySolution
x = {2y, 5y}
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