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Simplifying (6x + 4y)(-3x + -1y) = 0 Multiply (6x + 4y) * (-3x + -1y) (6x * (-3x + -1y) + 4y * (-3x + -1y)) = 0 ((-3x * 6x + -1y * 6x) + 4y * (-3x + -1y)) = 0 Reorder the terms: ((-6xy + -18x2) + 4y * (-3x + -1y)) = 0 ((-6xy + -18x2) + 4y * (-3x + -1y)) = 0 (-6xy + -18x2 + (-3x * 4y + -1y * 4y)) = 0 (-6xy + -18x2 + (-12xy + -4y2)) = 0 Reorder the terms: (-6xy + -12xy + -18x2 + -4y2) = 0 Combine like terms: -6xy + -12xy = -18xy (-18xy + -18x2 + -4y2) = 0 Solving -18xy + -18x2 + -4y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(9xy + 9x2 + 2y2) = 0 Factor a trinomial. -2((3x + y)(3x + 2y)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySubproblem 2
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySolution
x = {-0.3333333333y, -0.6666666667y}
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