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Simplifying (2x + -4y)(3x + -1y) = 0 Multiply (2x + -4y) * (3x + -1y) (2x * (3x + -1y) + -4y * (3x + -1y)) = 0 ((3x * 2x + -1y * 2x) + -4y * (3x + -1y)) = 0 Reorder the terms: ((-2xy + 6x^{2}) + -4y * (3x + -1y)) = 0 ((-2xy + 6x^{2}) + -4y * (3x + -1y)) = 0 (-2xy + 6x^{2}+ (3x * -4y + -1y * -4y)) = 0 (-2xy + 6x^{2}+ (-12xy + 4y^{2})) = 0 Reorder the terms: (-2xy + -12xy + 6x^{2}+ 4y^{2}) = 0 Combine like terms: -2xy + -12xy = -14xy (-14xy + 6x^{2}+ 4y^{2}) = 0 Solving -14xy + 6x^{2}+ 4y^{2}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7xy + 3x^{2}+ 2y^{2}) = 0 Factor a trinomial. 2((x + -2y)(3x + -1y)) = 0 Ignore the factor 2.## Subproblem 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 = 2y## Subproblem 2

Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333y## Solution

x = {2y, 0.3333333333y}

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