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Simplifying 5(b + a + -6c) + -7(c + -1b + 6a) = 0 Reorder the terms: 5(a + b + -6c) + -7(c + -1b + 6a) = 0 (a * 5 + b * 5 + -6c * 5) + -7(c + -1b + 6a) = 0 (5a + 5b + -30c) + -7(c + -1b + 6a) = 0 Reorder the terms: 5a + 5b + -30c + -7(6a + -1b + c) = 0 5a + 5b + -30c + (6a * -7 + -1b * -7 + c * -7) = 0 5a + 5b + -30c + (-42a + 7b + -7c) = 0 Reorder the terms: 5a + -42a + 5b + 7b + -30c + -7c = 0 Combine like terms: 5a + -42a = -37a -37a + 5b + 7b + -30c + -7c = 0 Combine like terms: 5b + 7b = 12b -37a + 12b + -30c + -7c = 0 Combine like terms: -30c + -7c = -37c -37a + 12b + -37c = 0 Solving -37a + 12b + -37c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12b' to each side of the equation. -37a + 12b + -12b + -37c = 0 + -12b Combine like terms: 12b + -12b = 0 -37a + 0 + -37c = 0 + -12b -37a + -37c = 0 + -12b Remove the zero: -37a + -37c = -12b Add '37c' to each side of the equation. -37a + -37c + 37c = -12b + 37c Combine like terms: -37c + 37c = 0 -37a + 0 = -12b + 37c -37a = -12b + 37c Divide each side by '-37'. a = 0.3243243243b + -1c Simplifying a = 0.3243243243b + -1c
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