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Simplifying (3x + 2y)(9x2 + -6xy + 4y2) = 0 Reorder the terms: (3x + 2y)(-6xy + 9x2 + 4y2) = 0 Multiply (3x + 2y) * (-6xy + 9x2 + 4y2) (3x * (-6xy + 9x2 + 4y2) + 2y * (-6xy + 9x2 + 4y2)) = 0 ((-6xy * 3x + 9x2 * 3x + 4y2 * 3x) + 2y * (-6xy + 9x2 + 4y2)) = 0 Reorder the terms: ((12xy2 + -18x2y + 27x3) + 2y * (-6xy + 9x2 + 4y2)) = 0 ((12xy2 + -18x2y + 27x3) + 2y * (-6xy + 9x2 + 4y2)) = 0 (12xy2 + -18x2y + 27x3 + (-6xy * 2y + 9x2 * 2y + 4y2 * 2y)) = 0 (12xy2 + -18x2y + 27x3 + (-12xy2 + 18x2y + 8y3)) = 0 Reorder the terms: (12xy2 + -12xy2 + -18x2y + 18x2y + 27x3 + 8y3) = 0 Combine like terms: 12xy2 + -12xy2 = 0 (0 + -18x2y + 18x2y + 27x3 + 8y3) = 0 (-18x2y + 18x2y + 27x3 + 8y3) = 0 Combine like terms: -18x2y + 18x2y = 0 (0 + 27x3 + 8y3) = 0 (27x3 + 8y3) = 0 Solving 27x3 + 8y3 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8y3' to each side of the equation. 27x3 + 8y3 + -8y3 = 0 + -8y3 Combine like terms: 8y3 + -8y3 = 0 27x3 + 0 = 0 + -8y3 27x3 = 0 + -8y3 Remove the zero: 27x3 = -8y3 Divide each side by '27'. x3 = -0.2962962963y3 Simplifying x3 = -0.2962962963y3 Combine like terms: -0.2962962963y3 + 0.2962962963y3 = 0.0000000000 x3 + 0.2962962963y3 = 0.0000000000 The solution to this equation could not be determined.
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