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Simplifying 9c(1c + -11) + 10(5c + -3) = 3c(1c + 5) + 1c(6c + -3) + -30 Reorder the terms: 9c(-11 + 1c) + 10(5c + -3) = 3c(1c + 5) + 1c(6c + -3) + -30 (-11 * 9c + 1c * 9c) + 10(5c + -3) = 3c(1c + 5) + 1c(6c + -3) + -30 (-99c + 9c2) + 10(5c + -3) = 3c(1c + 5) + 1c(6c + -3) + -30 Reorder the terms: -99c + 9c2 + 10(-3 + 5c) = 3c(1c + 5) + 1c(6c + -3) + -30 -99c + 9c2 + (-3 * 10 + 5c * 10) = 3c(1c + 5) + 1c(6c + -3) + -30 -99c + 9c2 + (-30 + 50c) = 3c(1c + 5) + 1c(6c + -3) + -30 Reorder the terms: -30 + -99c + 50c + 9c2 = 3c(1c + 5) + 1c(6c + -3) + -30 Combine like terms: -99c + 50c = -49c -30 + -49c + 9c2 = 3c(1c + 5) + 1c(6c + -3) + -30 Reorder the terms: -30 + -49c + 9c2 = 3c(5 + 1c) + 1c(6c + -3) + -30 -30 + -49c + 9c2 = (5 * 3c + 1c * 3c) + 1c(6c + -3) + -30 -30 + -49c + 9c2 = (15c + 3c2) + 1c(6c + -3) + -30 Reorder the terms: -30 + -49c + 9c2 = 15c + 3c2 + 1c(-3 + 6c) + -30 -30 + -49c + 9c2 = 15c + 3c2 + (-3 * 1c + 6c * 1c) + -30 -30 + -49c + 9c2 = 15c + 3c2 + (-3c + 6c2) + -30 Reorder the terms: -30 + -49c + 9c2 = -30 + 15c + -3c + 3c2 + 6c2 Combine like terms: 15c + -3c = 12c -30 + -49c + 9c2 = -30 + 12c + 3c2 + 6c2 Combine like terms: 3c2 + 6c2 = 9c2 -30 + -49c + 9c2 = -30 + 12c + 9c2 Add '30' to each side of the equation. -30 + -49c + 30 + 9c2 = -30 + 12c + 30 + 9c2 Reorder the terms: -30 + 30 + -49c + 9c2 = -30 + 12c + 30 + 9c2 Combine like terms: -30 + 30 = 0 0 + -49c + 9c2 = -30 + 12c + 30 + 9c2 -49c + 9c2 = -30 + 12c + 30 + 9c2 Reorder the terms: -49c + 9c2 = -30 + 30 + 12c + 9c2 Combine like terms: -30 + 30 = 0 -49c + 9c2 = 0 + 12c + 9c2 -49c + 9c2 = 12c + 9c2 Add '-9c2' to each side of the equation. -49c + 9c2 + -9c2 = 12c + 9c2 + -9c2 Combine like terms: 9c2 + -9c2 = 0 -49c + 0 = 12c + 9c2 + -9c2 -49c = 12c + 9c2 + -9c2 Combine like terms: 9c2 + -9c2 = 0 -49c = 12c + 0 -49c = 12c Solving -49c = 12c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-12c' to each side of the equation. -49c + -12c = 12c + -12c Combine like terms: -49c + -12c = -61c -61c = 12c + -12c Combine like terms: 12c + -12c = 0 -61c = 0 Divide each side by '-61'. c = 0 Simplifying c = 0
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