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Simplifying (x + -2y)(3x + 4y) = 0 Multiply (x + -2y) * (3x + 4y) (x(3x + 4y) + -2y * (3x + 4y)) = 0 ((3x * x + 4y * x) + -2y * (3x + 4y)) = 0 Reorder the terms: ((4xy + 3x2) + -2y * (3x + 4y)) = 0 ((4xy + 3x2) + -2y * (3x + 4y)) = 0 (4xy + 3x2 + (3x * -2y + 4y * -2y)) = 0 (4xy + 3x2 + (-6xy + -8y2)) = 0 Reorder the terms: (4xy + -6xy + 3x2 + -8y2) = 0 Combine like terms: 4xy + -6xy = -2xy (-2xy + 3x2 + -8y2) = 0 Solving -2xy + 3x2 + -8y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -2y)(3x + 4y) = 0Subproblem 1
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 = 2ySubproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve: Simplifying 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySolution
x = {2y, -1.333333333y}
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