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Simplifying 3x(4x + 2y) + -2y(3x + -4y) = 0 (4x * 3x + 2y * 3x) + -2y(3x + -4y) = 0 Reorder the terms: (6xy + 12x2) + -2y(3x + -4y) = 0 (6xy + 12x2) + -2y(3x + -4y) = 0 6xy + 12x2 + (3x * -2y + -4y * -2y) = 0 6xy + 12x2 + (-6xy + 8y2) = 0 Reorder the terms: 6xy + -6xy + 12x2 + 8y2 = 0 Combine like terms: 6xy + -6xy = 0 0 + 12x2 + 8y2 = 0 12x2 + 8y2 = 0 Solving 12x2 + 8y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8y2' to each side of the equation. 12x2 + 8y2 + -8y2 = 0 + -8y2 Combine like terms: 8y2 + -8y2 = 0 12x2 + 0 = 0 + -8y2 12x2 = 0 + -8y2 Remove the zero: 12x2 = -8y2 Divide each side by '12'. x2 = -0.6666666667y2 Simplifying x2 = -0.6666666667y2 Combine like terms: -0.6666666667y2 + 0.6666666667y2 = 0.0000000000 x2 + 0.6666666667y2 = 0.0000000000 The solution to this equation could not be determined.
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