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Simplifying (7a + -12b + 4c) + -1(-8a + 15b + -9c) = 0 Remove parenthesis around (7a + -12b + 4c) 7a + -12b + 4c + -1(-8a + 15b + -9c) = 0 7a + -12b + 4c + (-8a * -1 + 15b * -1 + -9c * -1) = 0 7a + -12b + 4c + (8a + -15b + 9c) = 0 Reorder the terms: 7a + 8a + -12b + -15b + 4c + 9c = 0 Combine like terms: 7a + 8a = 15a 15a + -12b + -15b + 4c + 9c = 0 Combine like terms: -12b + -15b = -27b 15a + -27b + 4c + 9c = 0 Combine like terms: 4c + 9c = 13c 15a + -27b + 13c = 0 Solving 15a + -27b + 13c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '27b' to each side of the equation. 15a + -27b + 27b + 13c = 0 + 27b Combine like terms: -27b + 27b = 0 15a + 0 + 13c = 0 + 27b 15a + 13c = 0 + 27b Remove the zero: 15a + 13c = 27b Add '-13c' to each side of the equation. 15a + 13c + -13c = 27b + -13c Combine like terms: 13c + -13c = 0 15a + 0 = 27b + -13c 15a = 27b + -13c Divide each side by '15'. a = 1.8b + -0.8666666667c Simplifying a = 1.8b + -0.8666666667c
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