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Simplifying (c + -5)(2c + 7) = 0 Reorder the terms: (-5 + c)(2c + 7) = 0 Reorder the terms: (-5 + c)(7 + 2c) = 0 Multiply (-5 + c) * (7 + 2c) (-5(7 + 2c) + c(7 + 2c)) = 0 ((7 * -5 + 2c * -5) + c(7 + 2c)) = 0 ((-35 + -10c) + c(7 + 2c)) = 0 (-35 + -10c + (7 * c + 2c * c)) = 0 (-35 + -10c + (7c + 2c2)) = 0 Combine like terms: -10c + 7c = -3c (-35 + -3c + 2c2) = 0 Solving -35 + -3c + 2c2 = 0 Solving for variable 'c'. Factor a trinomial. (-7 + -2c)(5 + -1c) = 0Subproblem 1
Set the factor '(-7 + -2c)' equal to zero and attempt to solve: Simplifying -7 + -2c = 0 Solving -7 + -2c = 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 + -2c = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2c = 0 + 7 -2c = 0 + 7 Combine like terms: 0 + 7 = 7 -2c = 7 Divide each side by '-2'. c = -3.5 Simplifying c = -3.5Subproblem 2
Set the factor '(5 + -1c)' equal to zero and attempt to solve: Simplifying 5 + -1c = 0 Solving 5 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1c = 0 + -5 -1c = 0 + -5 Combine like terms: 0 + -5 = -5 -1c = -5 Divide each side by '-1'. c = 5 Simplifying c = 5Solution
c = {-3.5, 5}
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