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Simplifying (c + 24)(c + -30) = 0 Reorder the terms: (24 + c)(c + -30) = 0 Reorder the terms: (24 + c)(-30 + c) = 0 Multiply (24 + c) * (-30 + c) (24(-30 + c) + c(-30 + c)) = 0 ((-30 * 24 + c * 24) + c(-30 + c)) = 0 ((-720 + 24c) + c(-30 + c)) = 0 (-720 + 24c + (-30 * c + c * c)) = 0 (-720 + 24c + (-30c + c2)) = 0 Combine like terms: 24c + -30c = -6c (-720 + -6c + c2) = 0 Solving -720 + -6c + c2 = 0 Solving for variable 'c'. Factor a trinomial. (-24 + -1c)(30 + -1c) = 0Subproblem 1
Set the factor '(-24 + -1c)' equal to zero and attempt to solve: Simplifying -24 + -1c = 0 Solving -24 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1c = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1c = 0 + 24 -1c = 0 + 24 Combine like terms: 0 + 24 = 24 -1c = 24 Divide each side by '-1'. c = -24 Simplifying c = -24Subproblem 2
Set the factor '(30 + -1c)' equal to zero and attempt to solve: Simplifying 30 + -1c = 0 Solving 30 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1c = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1c = 0 + -30 -1c = 0 + -30 Combine like terms: 0 + -30 = -30 -1c = -30 Divide each side by '-1'. c = 30 Simplifying c = 30Solution
c = {-24, 30}
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