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Simplifying (2x + 4y)(3x + 5y) = 0 Multiply (2x + 4y) * (3x + 5y) (2x * (3x + 5y) + 4y * (3x + 5y)) = 0 ((3x * 2x + 5y * 2x) + 4y * (3x + 5y)) = 0 Reorder the terms: ((10xy + 6x2) + 4y * (3x + 5y)) = 0 ((10xy + 6x2) + 4y * (3x + 5y)) = 0 (10xy + 6x2 + (3x * 4y + 5y * 4y)) = 0 (10xy + 6x2 + (12xy + 20y2)) = 0 Reorder the terms: (10xy + 12xy + 6x2 + 20y2) = 0 Combine like terms: 10xy + 12xy = 22xy (22xy + 6x2 + 20y2) = 0 Solving 22xy + 6x2 + 20y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11xy + 3x2 + 10y2) = 0 Factor a trinomial. 2((3x + 5y)(x + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3x + 5y)' equal to zero and attempt to solve: Simplifying 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 = -1.666666667ySubproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySolution
x = {-1.666666667y, -2y}
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