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Simplifying 5(2b + 3c + -10d + 2) = 0 Reorder the terms: 5(2 + 2b + 3c + -10d) = 0 (2 * 5 + 2b * 5 + 3c * 5 + -10d * 5) = 0 (10 + 10b + 15c + -50d) = 0 Solving 10 + 10b + 15c + -50d = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + 10b + 15c + -10 + -50d = 0 + -10 Reorder the terms: 10 + -10 + 10b + 15c + -50d = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10b + 15c + -50d = 0 + -10 10b + 15c + -50d = 0 + -10 Combine like terms: 0 + -10 = -10 10b + 15c + -50d = -10 Add '-15c' to each side of the equation. 10b + 15c + -15c + -50d = -10 + -15c Combine like terms: 15c + -15c = 0 10b + 0 + -50d = -10 + -15c 10b + -50d = -10 + -15c Add '50d' to each side of the equation. 10b + -50d + 50d = -10 + -15c + 50d Combine like terms: -50d + 50d = 0 10b + 0 = -10 + -15c + 50d 10b = -10 + -15c + 50d Divide each side by '10'. b = -1 + -1.5c + 5d Simplifying b = -1 + -1.5c + 5d
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