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Simplifying (6 + -2c)(c + -5) + -1(-2c + 1)(c + -2) = 0 Reorder the terms: (6 + -2c)(-5 + c) + -1(-2c + 1)(c + -2) = 0 Multiply (6 + -2c) * (-5 + c) (6(-5 + c) + -2c * (-5 + c)) + -1(-2c + 1)(c + -2) = 0 ((-5 * 6 + c * 6) + -2c * (-5 + c)) + -1(-2c + 1)(c + -2) = 0 ((-30 + 6c) + -2c * (-5 + c)) + -1(-2c + 1)(c + -2) = 0 (-30 + 6c + (-5 * -2c + c * -2c)) + -1(-2c + 1)(c + -2) = 0 (-30 + 6c + (10c + -2c2)) + -1(-2c + 1)(c + -2) = 0 Combine like terms: 6c + 10c = 16c (-30 + 16c + -2c2) + -1(-2c + 1)(c + -2) = 0 Reorder the terms: -30 + 16c + -2c2 + -1(1 + -2c)(c + -2) = 0 Reorder the terms: -30 + 16c + -2c2 + -1(1 + -2c)(-2 + c) = 0 Multiply (1 + -2c) * (-2 + c) -30 + 16c + -2c2 + -1(1(-2 + c) + -2c * (-2 + c)) = 0 -30 + 16c + -2c2 + -1((-2 * 1 + c * 1) + -2c * (-2 + c)) = 0 -30 + 16c + -2c2 + -1((-2 + 1c) + -2c * (-2 + c)) = 0 -30 + 16c + -2c2 + -1(-2 + 1c + (-2 * -2c + c * -2c)) = 0 -30 + 16c + -2c2 + -1(-2 + 1c + (4c + -2c2)) = 0 Combine like terms: 1c + 4c = 5c -30 + 16c + -2c2 + -1(-2 + 5c + -2c2) = 0 -30 + 16c + -2c2 + (-2 * -1 + 5c * -1 + -2c2 * -1) = 0 -30 + 16c + -2c2 + (2 + -5c + 2c2) = 0 Reorder the terms: -30 + 2 + 16c + -5c + -2c2 + 2c2 = 0 Combine like terms: -30 + 2 = -28 -28 + 16c + -5c + -2c2 + 2c2 = 0 Combine like terms: 16c + -5c = 11c -28 + 11c + -2c2 + 2c2 = 0 Combine like terms: -2c2 + 2c2 = 0 -28 + 11c + 0 = 0 -28 + 11c = 0 Solving -28 + 11c = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 11c = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 11c = 0 + 28 11c = 0 + 28 Combine like terms: 0 + 28 = 28 11c = 28 Divide each side by '11'. c = 2.545454545 Simplifying c = 2.545454545
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