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Simplifying (8c + 5)(3c + -9) = 0 Reorder the terms: (5 + 8c)(3c + -9) = 0 Reorder the terms: (5 + 8c)(-9 + 3c) = 0 Multiply (5 + 8c) * (-9 + 3c) (5(-9 + 3c) + 8c * (-9 + 3c)) = 0 ((-9 * 5 + 3c * 5) + 8c * (-9 + 3c)) = 0 ((-45 + 15c) + 8c * (-9 + 3c)) = 0 (-45 + 15c + (-9 * 8c + 3c * 8c)) = 0 (-45 + 15c + (-72c + 24c2)) = 0 Combine like terms: 15c + -72c = -57c (-45 + -57c + 24c2) = 0 Solving -45 + -57c + 24c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -19c + 8c2) = 0 Factor a trinomial. 3((-5 + -8c)(3 + -1c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -8c)' equal to zero and attempt to solve: Simplifying -5 + -8c = 0 Solving -5 + -8c = 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 + -8c = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8c = 0 + 5 -8c = 0 + 5 Combine like terms: 0 + 5 = 5 -8c = 5 Divide each side by '-8'. c = -0.625 Simplifying c = -0.625Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve: Simplifying 3 + -1c = 0 Solving 3 + -1c = 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 + -1c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1c = 0 + -3 -1c = 0 + -3 Combine like terms: 0 + -3 = -3 -1c = -3 Divide each side by '-1'. c = 3 Simplifying c = 3Solution
c = {-0.625, 3}
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