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Simplifying (12a + -3b + -5c) + -5(-5a + 4b + -6c) = 0 Remove parenthesis around (12a + -3b + -5c) 12a + -3b + -5c + -5(-5a + 4b + -6c) = 0 12a + -3b + -5c + (-5a * -5 + 4b * -5 + -6c * -5) = 0 12a + -3b + -5c + (25a + -20b + 30c) = 0 Reorder the terms: 12a + 25a + -3b + -20b + -5c + 30c = 0 Combine like terms: 12a + 25a = 37a 37a + -3b + -20b + -5c + 30c = 0 Combine like terms: -3b + -20b = -23b 37a + -23b + -5c + 30c = 0 Combine like terms: -5c + 30c = 25c 37a + -23b + 25c = 0 Solving 37a + -23b + 25c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '23b' to each side of the equation. 37a + -23b + 23b + 25c = 0 + 23b Combine like terms: -23b + 23b = 0 37a + 0 + 25c = 0 + 23b 37a + 25c = 0 + 23b Remove the zero: 37a + 25c = 23b Add '-25c' to each side of the equation. 37a + 25c + -25c = 23b + -25c Combine like terms: 25c + -25c = 0 37a + 0 = 23b + -25c 37a = 23b + -25c Divide each side by '37'. a = 0.6216216216b + -0.6756756757c Simplifying a = 0.6216216216b + -0.6756756757c
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