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Simplifying 5(9b + c + -9a) + -7(a + -8c + 8b) = 0 Reorder the terms: 5(-9a + 9b + c) + -7(a + -8c + 8b) = 0 (-9a * 5 + 9b * 5 + c * 5) + -7(a + -8c + 8b) = 0 (-45a + 45b + 5c) + -7(a + -8c + 8b) = 0 Reorder the terms: -45a + 45b + 5c + -7(a + 8b + -8c) = 0 -45a + 45b + 5c + (a * -7 + 8b * -7 + -8c * -7) = 0 -45a + 45b + 5c + (-7a + -56b + 56c) = 0 Reorder the terms: -45a + -7a + 45b + -56b + 5c + 56c = 0 Combine like terms: -45a + -7a = -52a -52a + 45b + -56b + 5c + 56c = 0 Combine like terms: 45b + -56b = -11b -52a + -11b + 5c + 56c = 0 Combine like terms: 5c + 56c = 61c -52a + -11b + 61c = 0 Solving -52a + -11b + 61c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11b' to each side of the equation. -52a + -11b + 11b + 61c = 0 + 11b Combine like terms: -11b + 11b = 0 -52a + 0 + 61c = 0 + 11b -52a + 61c = 0 + 11b Remove the zero: -52a + 61c = 11b Add '-61c' to each side of the equation. -52a + 61c + -61c = 11b + -61c Combine like terms: 61c + -61c = 0 -52a + 0 = 11b + -61c -52a = 11b + -61c Divide each side by '-52'. a = -0.2115384615b + 1.173076923c Simplifying a = -0.2115384615b + 1.173076923c
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