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Simplifying (2c + -1)(5c + -7) = 0 Reorder the terms: (-1 + 2c)(5c + -7) = 0 Reorder the terms: (-1 + 2c)(-7 + 5c) = 0 Multiply (-1 + 2c) * (-7 + 5c) (-1(-7 + 5c) + 2c * (-7 + 5c)) = 0 ((-7 * -1 + 5c * -1) + 2c * (-7 + 5c)) = 0 ((7 + -5c) + 2c * (-7 + 5c)) = 0 (7 + -5c + (-7 * 2c + 5c * 2c)) = 0 (7 + -5c + (-14c + 10c2)) = 0 Combine like terms: -5c + -14c = -19c (7 + -19c + 10c2) = 0 Solving 7 + -19c + 10c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -2c)(7 + -5c) = 0Subproblem 1
Set the factor '(1 + -2c)' equal to zero and attempt to solve: Simplifying 1 + -2c = 0 Solving 1 + -2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2c = 0 + -1 -2c = 0 + -1 Combine like terms: 0 + -1 = -1 -2c = -1 Divide each side by '-2'. c = 0.5 Simplifying c = 0.5Subproblem 2
Set the factor '(7 + -5c)' equal to zero and attempt to solve: Simplifying 7 + -5c = 0 Solving 7 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5c = 0 + -7 -5c = 0 + -7 Combine like terms: 0 + -7 = -7 -5c = -7 Divide each side by '-5'. c = 1.4 Simplifying c = 1.4Solution
c = {0.5, 1.4}
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