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Simplifying 0.3(15d + 3c) + -0.5(8c + -10d) = 0 Reorder the terms: 0.3(3c + 15d) + -0.5(8c + -10d) = 0 (3c * 0.3 + 15d * 0.3) + -0.5(8c + -10d) = 0 (0.9c + 4.5d) + -0.5(8c + -10d) = 0 0.9c + 4.5d + (8c * -0.5 + -10d * -0.5) = 0 0.9c + 4.5d + (-4c + 5d) = 0 Reorder the terms: 0.9c + -4c + 4.5d + 5d = 0 Combine like terms: 0.9c + -4c = -3.1c -3.1c + 4.5d + 5d = 0 Combine like terms: 4.5d + 5d = 9.5d -3.1c + 9.5d = 0 Solving -3.1c + 9.5d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-9.5d' to each side of the equation. -3.1c + 9.5d + -9.5d = 0 + -9.5d Combine like terms: 9.5d + -9.5d = 0.0 -3.1c + 0.0 = 0 + -9.5d -3.1c = 0 + -9.5d Remove the zero: -3.1c = -9.5d Divide each side by '-3.1'. c = 3.064516129d Simplifying c = 3.064516129d
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