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Simplifying 8(3a + 7c) + -6(2a + 4c) = 0 (3a * 8 + 7c * 8) + -6(2a + 4c) = 0 (24a + 56c) + -6(2a + 4c) = 0 24a + 56c + (2a * -6 + 4c * -6) = 0 24a + 56c + (-12a + -24c) = 0 Reorder the terms: 24a + -12a + 56c + -24c = 0 Combine like terms: 24a + -12a = 12a 12a + 56c + -24c = 0 Combine like terms: 56c + -24c = 32c 12a + 32c = 0 Solving 12a + 32c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-32c' to each side of the equation. 12a + 32c + -32c = 0 + -32c Combine like terms: 32c + -32c = 0 12a + 0 = 0 + -32c 12a = 0 + -32c Remove the zero: 12a = -32c Divide each side by '12'. a = -2.666666667c Simplifying a = -2.666666667c
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