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Simplifying (-2c + 7)(4c + -5) = 0 Reorder the terms: (7 + -2c)(4c + -5) = 0 Reorder the terms: (7 + -2c)(-5 + 4c) = 0 Multiply (7 + -2c) * (-5 + 4c) (7(-5 + 4c) + -2c * (-5 + 4c)) = 0 ((-5 * 7 + 4c * 7) + -2c * (-5 + 4c)) = 0 ((-35 + 28c) + -2c * (-5 + 4c)) = 0 (-35 + 28c + (-5 * -2c + 4c * -2c)) = 0 (-35 + 28c + (10c + -8c2)) = 0 Combine like terms: 28c + 10c = 38c (-35 + 38c + -8c2) = 0 Solving -35 + 38c + -8c2 = 0 Solving for variable 'c'. Factor a trinomial. (-7 + 2c)(5 + -4c) = 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 + -4c)' equal to zero and attempt to solve: Simplifying 5 + -4c = 0 Solving 5 + -4c = 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 + -4c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4c = 0 + -5 -4c = 0 + -5 Combine like terms: 0 + -5 = -5 -4c = -5 Divide each side by '-4'. c = 1.25 Simplifying c = 1.25Solution
c = {3.5, 1.25}
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