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Simplifying 9(2C + 5) * 3C = -75 Reorder the terms: 9(5 + 2C) * 3C = -75 Reorder the terms for easier multiplication: 9 * 3C(5 + 2C) = -75 Multiply 9 * 3 27C(5 + 2C) = -75 (5 * 27C + 2C * 27C) = -75 (135C + 54C2) = -75 Solving 135C + 54C2 = -75 Solving for variable 'C'. Reorder the terms: 75 + 135C + 54C2 = -75 + 75 Combine like terms: -75 + 75 = 0 75 + 135C + 54C2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + 45C + 18C2) = 0 Factor a trinomial. 3((5 + 3C)(5 + 6C)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 3C)' equal to zero and attempt to solve: Simplifying 5 + 3C = 0 Solving 5 + 3C = 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 + 3C = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3C = 0 + -5 3C = 0 + -5 Combine like terms: 0 + -5 = -5 3C = -5 Divide each side by '3'. C = -1.666666667 Simplifying C = -1.666666667Subproblem 2
Set the factor '(5 + 6C)' equal to zero and attempt to solve: Simplifying 5 + 6C = 0 Solving 5 + 6C = 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 + 6C = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6C = 0 + -5 6C = 0 + -5 Combine like terms: 0 + -5 = -5 6C = -5 Divide each side by '6'. C = -0.8333333333 Simplifying C = -0.8333333333Solution
C = {-1.666666667, -0.8333333333}
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