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Simplifying (-8a + 15b + -9c) + -1(7a + -12b + 4c) = 0 Remove parenthesis around (-8a + 15b + -9c) -8a + 15b + -9c + -1(7a + -12b + 4c) = 0 -8a + 15b + -9c + (7a * -1 + -12b * -1 + 4c * -1) = 0 -8a + 15b + -9c + (-7a + 12b + -4c) = 0 Reorder the terms: -8a + -7a + 15b + 12b + -9c + -4c = 0 Combine like terms: -8a + -7a = -15a -15a + 15b + 12b + -9c + -4c = 0 Combine like terms: 15b + 12b = 27b -15a + 27b + -9c + -4c = 0 Combine like terms: -9c + -4c = -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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