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Simplifying (3a + 2c)(9a2 + -6ac + 4c2) = 0 Reorder the terms: (3a + 2c)(-6ac + 9a2 + 4c2) = 0 Multiply (3a + 2c) * (-6ac + 9a2 + 4c2) (3a * (-6ac + 9a2 + 4c2) + 2c * (-6ac + 9a2 + 4c2)) = 0 ((-6ac * 3a + 9a2 * 3a + 4c2 * 3a) + 2c * (-6ac + 9a2 + 4c2)) = 0 Reorder the terms: ((12ac2 + -18a2c + 27a3) + 2c * (-6ac + 9a2 + 4c2)) = 0 ((12ac2 + -18a2c + 27a3) + 2c * (-6ac + 9a2 + 4c2)) = 0 (12ac2 + -18a2c + 27a3 + (-6ac * 2c + 9a2 * 2c + 4c2 * 2c)) = 0 (12ac2 + -18a2c + 27a3 + (-12ac2 + 18a2c + 8c3)) = 0 Reorder the terms: (12ac2 + -12ac2 + -18a2c + 18a2c + 27a3 + 8c3) = 0 Combine like terms: 12ac2 + -12ac2 = 0 (0 + -18a2c + 18a2c + 27a3 + 8c3) = 0 (-18a2c + 18a2c + 27a3 + 8c3) = 0 Combine like terms: -18a2c + 18a2c = 0 (0 + 27a3 + 8c3) = 0 (27a3 + 8c3) = 0 Solving 27a3 + 8c3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8c3' to each side of the equation. 27a3 + 8c3 + -8c3 = 0 + -8c3 Combine like terms: 8c3 + -8c3 = 0 27a3 + 0 = 0 + -8c3 27a3 = 0 + -8c3 Remove the zero: 27a3 = -8c3 Divide each side by '27'. a3 = -0.2962962963c3 Simplifying a3 = -0.2962962963c3 Combine like terms: -0.2962962963c3 + 0.2962962963c3 = 0.0000000000 a3 + 0.2962962963c3 = 0.0000000000 The solution to this equation could not be determined.
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