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Simplifying (-2c + 3d)(-5) + 3(-2c) + -1(-8) = 0 Reorder the terms for easier multiplication: -5(-2c + 3d) + 3(-2c) + -1(-8) = 0 (-2c * -5 + 3d * -5) + 3(-2c) + -1(-8) = 0 (10c + -15d) + 3(-2c) + -1(-8) = 0 Remove parenthesis around (-2c) 10c + -15d + 3 * -2c + -1(-8) = 0 Multiply 3 * -2 10c + -15d + -6c + -1(-8) = 0 Multiply -1 * -8 10c + -15d + -6c + 8 = 0 Reorder the terms: 8 + 10c + -6c + -15d = 0 Combine like terms: 10c + -6c = 4c 8 + 4c + -15d = 0 Solving 8 + 4c + -15d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 4c + -8 + -15d = 0 + -8 Reorder the terms: 8 + -8 + 4c + -15d = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4c + -15d = 0 + -8 4c + -15d = 0 + -8 Combine like terms: 0 + -8 = -8 4c + -15d = -8 Add '15d' to each side of the equation. 4c + -15d + 15d = -8 + 15d Combine like terms: -15d + 15d = 0 4c + 0 = -8 + 15d 4c = -8 + 15d Divide each side by '4'. c = -2 + 3.75d Simplifying c = -2 + 3.75d
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