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Simplifying (5c + -1)(6c + -7) = 0 Reorder the terms: (-1 + 5c)(6c + -7) = 0 Reorder the terms: (-1 + 5c)(-7 + 6c) = 0 Multiply (-1 + 5c) * (-7 + 6c) (-1(-7 + 6c) + 5c * (-7 + 6c)) = 0 ((-7 * -1 + 6c * -1) + 5c * (-7 + 6c)) = 0 ((7 + -6c) + 5c * (-7 + 6c)) = 0 (7 + -6c + (-7 * 5c + 6c * 5c)) = 0 (7 + -6c + (-35c + 30c2)) = 0 Combine like terms: -6c + -35c = -41c (7 + -41c + 30c2) = 0 Solving 7 + -41c + 30c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -5c)(7 + -6c) = 0Subproblem 1
Set the factor '(1 + -5c)' equal to zero and attempt to solve: Simplifying 1 + -5c = 0 Solving 1 + -5c = 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 + -5c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5c = 0 + -1 -5c = 0 + -1 Combine like terms: 0 + -1 = -1 -5c = -1 Divide each side by '-5'. c = 0.2 Simplifying c = 0.2Subproblem 2
Set the factor '(7 + -6c)' equal to zero and attempt to solve: Simplifying 7 + -6c = 0 Solving 7 + -6c = 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 + -6c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6c = 0 + -7 -6c = 0 + -7 Combine like terms: 0 + -7 = -7 -6c = -7 Divide each side by '-6'. c = 1.166666667 Simplifying c = 1.166666667Solution
c = {0.2, 1.166666667}
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