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Simplifying 8(4a + 8c) + -6(2a + 6c) = 0 (4a * 8 + 8c * 8) + -6(2a + 6c) = 0 (32a + 64c) + -6(2a + 6c) = 0 32a + 64c + (2a * -6 + 6c * -6) = 0 32a + 64c + (-12a + -36c) = 0 Reorder the terms: 32a + -12a + 64c + -36c = 0 Combine like terms: 32a + -12a = 20a 20a + 64c + -36c = 0 Combine like terms: 64c + -36c = 28c 20a + 28c = 0 Solving 20a + 28c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-28c' to each side of the equation. 20a + 28c + -28c = 0 + -28c Combine like terms: 28c + -28c = 0 20a + 0 = 0 + -28c 20a = 0 + -28c Remove the zero: 20a = -28c Divide each side by '20'. a = -1.4c Simplifying a = -1.4c
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