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Simplifying 0.5(-12 + 6) + -3(c + 4) + 10(c + -5) = 0 Combine like terms: -12 + 6 = -6 0.5(-6) + -3(c + 4) + 10(c + -5) = 0 Multiply 0.5 * -6 -3 + -3(c + 4) + 10(c + -5) = 0 Reorder the terms: -3 + -3(4 + c) + 10(c + -5) = 0 -3 + (4 * -3 + c * -3) + 10(c + -5) = 0 -3 + (-12 + -3c) + 10(c + -5) = 0 Reorder the terms: -3 + -12 + -3c + 10(-5 + c) = 0 -3 + -12 + -3c + (-5 * 10 + c * 10) = 0 -3 + -12 + -3c + (-50 + 10c) = 0 Reorder the terms: -3 + -12 + -50 + -3c + 10c = 0 Combine like terms: -3 + -12 = -15 -15 + -50 + -3c + 10c = 0 Combine like terms: -15 + -50 = -65 -65 + -3c + 10c = 0 Combine like terms: -3c + 10c = 7c -65 + 7c = 0 Solving -65 + 7c = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + 7c = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 7c = 0 + 65 7c = 0 + 65 Combine like terms: 0 + 65 = 65 7c = 65 Divide each side by '7'. c = 9.285714286 Simplifying c = 9.285714286
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