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Simplifying (3c + 8)(8c + -3) = 0 Reorder the terms: (8 + 3c)(8c + -3) = 0 Reorder the terms: (8 + 3c)(-3 + 8c) = 0 Multiply (8 + 3c) * (-3 + 8c) (8(-3 + 8c) + 3c * (-3 + 8c)) = 0 ((-3 * 8 + 8c * 8) + 3c * (-3 + 8c)) = 0 ((-24 + 64c) + 3c * (-3 + 8c)) = 0 (-24 + 64c + (-3 * 3c + 8c * 3c)) = 0 (-24 + 64c + (-9c + 24c2)) = 0 Combine like terms: 64c + -9c = 55c (-24 + 55c + 24c2) = 0 Solving -24 + 55c + 24c2 = 0 Solving for variable 'c'. Factor a trinomial. (-8 + -3c)(3 + -8c) = 0Subproblem 1
Set the factor '(-8 + -3c)' equal to zero and attempt to solve: Simplifying -8 + -3c = 0 Solving -8 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3c = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3c = 0 + 8 -3c = 0 + 8 Combine like terms: 0 + 8 = 8 -3c = 8 Divide each side by '-3'. c = -2.666666667 Simplifying c = -2.666666667Subproblem 2
Set the factor '(3 + -8c)' equal to zero and attempt to solve: Simplifying 3 + -8c = 0 Solving 3 + -8c = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8c = 0 + -3 -8c = 0 + -3 Combine like terms: 0 + -3 = -3 -8c = -3 Divide each side by '-8'. c = 0.375 Simplifying c = 0.375Solution
c = {-2.666666667, 0.375}
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