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Simplifying 3(b + 4c) + -1(c + -1b) = 0 (b * 3 + 4c * 3) + -1(c + -1b) = 0 (3b + 12c) + -1(c + -1b) = 0 Reorder the terms: 3b + 12c + -1(-1b + c) = 0 3b + 12c + (-1b * -1 + c * -1) = 0 3b + 12c + (1b + -1c) = 0 Reorder the terms: 3b + 1b + 12c + -1c = 0 Combine like terms: 3b + 1b = 4b 4b + 12c + -1c = 0 Combine like terms: 12c + -1c = 11c 4b + 11c = 0 Solving 4b + 11c = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-11c' to each side of the equation. 4b + 11c + -11c = 0 + -11c Combine like terms: 11c + -11c = 0 4b + 0 = 0 + -11c 4b = 0 + -11c Remove the zero: 4b = -11c Divide each side by '4'. b = -2.75c Simplifying b = -2.75c
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