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Simplifying 9c(c + -11) + 10(5c + -3) = 3c(c + 5) + c(6c + -30) + -30 Reorder the terms: 9c(-11 + c) + 10(5c + -3) = 3c(c + 5) + c(6c + -30) + -30 (-11 * 9c + c * 9c) + 10(5c + -3) = 3c(c + 5) + c(6c + -30) + -30 (-99c + 9c2) + 10(5c + -3) = 3c(c + 5) + c(6c + -30) + -30 Reorder the terms: -99c + 9c2 + 10(-3 + 5c) = 3c(c + 5) + c(6c + -30) + -30 -99c + 9c2 + (-3 * 10 + 5c * 10) = 3c(c + 5) + c(6c + -30) + -30 -99c + 9c2 + (-30 + 50c) = 3c(c + 5) + c(6c + -30) + -30 Reorder the terms: -30 + -99c + 50c + 9c2 = 3c(c + 5) + c(6c + -30) + -30 Combine like terms: -99c + 50c = -49c -30 + -49c + 9c2 = 3c(c + 5) + c(6c + -30) + -30 Reorder the terms: -30 + -49c + 9c2 = 3c(5 + c) + c(6c + -30) + -30 -30 + -49c + 9c2 = (5 * 3c + c * 3c) + c(6c + -30) + -30 -30 + -49c + 9c2 = (15c + 3c2) + c(6c + -30) + -30 Reorder the terms: -30 + -49c + 9c2 = 15c + 3c2 + c(-30 + 6c) + -30 -30 + -49c + 9c2 = 15c + 3c2 + (-30 * c + 6c * c) + -30 -30 + -49c + 9c2 = 15c + 3c2 + (-30c + 6c2) + -30 Reorder the terms: -30 + -49c + 9c2 = -30 + 15c + -30c + 3c2 + 6c2 Combine like terms: 15c + -30c = -15c -30 + -49c + 9c2 = -30 + -15c + 3c2 + 6c2 Combine like terms: 3c2 + 6c2 = 9c2 -30 + -49c + 9c2 = -30 + -15c + 9c2 Add '30' to each side of the equation. -30 + -49c + 30 + 9c2 = -30 + -15c + 30 + 9c2 Reorder the terms: -30 + 30 + -49c + 9c2 = -30 + -15c + 30 + 9c2 Combine like terms: -30 + 30 = 0 0 + -49c + 9c2 = -30 + -15c + 30 + 9c2 -49c + 9c2 = -30 + -15c + 30 + 9c2 Reorder the terms: -49c + 9c2 = -30 + 30 + -15c + 9c2 Combine like terms: -30 + 30 = 0 -49c + 9c2 = 0 + -15c + 9c2 -49c + 9c2 = -15c + 9c2 Add '-9c2' to each side of the equation. -49c + 9c2 + -9c2 = -15c + 9c2 + -9c2 Combine like terms: 9c2 + -9c2 = 0 -49c + 0 = -15c + 9c2 + -9c2 -49c = -15c + 9c2 + -9c2 Combine like terms: 9c2 + -9c2 = 0 -49c = -15c + 0 -49c = -15c Solving -49c = -15c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '15c' to each side of the equation. -49c + 15c = -15c + 15c Combine like terms: -49c + 15c = -34c -34c = -15c + 15c Combine like terms: -15c + 15c = 0 -34c = 0 Divide each side by '-34'. c = 0 Simplifying c = 0
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