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Simplifying 3(5c + -1) + 9 = (6c + 1)(6c + 1) Reorder the terms: 3(-1 + 5c) + 9 = (6c + 1)(6c + 1) (-1 * 3 + 5c * 3) + 9 = (6c + 1)(6c + 1) (-3 + 15c) + 9 = (6c + 1)(6c + 1) Reorder the terms: -3 + 9 + 15c = (6c + 1)(6c + 1) Combine like terms: -3 + 9 = 6 6 + 15c = (6c + 1)(6c + 1) Reorder the terms: 6 + 15c = (1 + 6c)(6c + 1) Reorder the terms: 6 + 15c = (1 + 6c)(1 + 6c) Multiply (1 + 6c) * (1 + 6c) 6 + 15c = (1(1 + 6c) + 6c * (1 + 6c)) 6 + 15c = ((1 * 1 + 6c * 1) + 6c * (1 + 6c)) 6 + 15c = ((1 + 6c) + 6c * (1 + 6c)) 6 + 15c = (1 + 6c + (1 * 6c + 6c * 6c)) 6 + 15c = (1 + 6c + (6c + 36c2)) Combine like terms: 6c + 6c = 12c 6 + 15c = (1 + 12c + 36c2) Solving 6 + 15c = 1 + 12c + 36c2 Solving for variable 'c'. Reorder the terms: 6 + -1 + 15c + -12c + -36c2 = 1 + 12c + 36c2 + -1 + -12c + -36c2 Combine like terms: 6 + -1 = 5 5 + 15c + -12c + -36c2 = 1 + 12c + 36c2 + -1 + -12c + -36c2 Combine like terms: 15c + -12c = 3c 5 + 3c + -36c2 = 1 + 12c + 36c2 + -1 + -12c + -36c2 Reorder the terms: 5 + 3c + -36c2 = 1 + -1 + 12c + -12c + 36c2 + -36c2 Combine like terms: 1 + -1 = 0 5 + 3c + -36c2 = 0 + 12c + -12c + 36c2 + -36c2 5 + 3c + -36c2 = 12c + -12c + 36c2 + -36c2 Combine like terms: 12c + -12c = 0 5 + 3c + -36c2 = 0 + 36c2 + -36c2 5 + 3c + -36c2 = 36c2 + -36c2 Combine like terms: 36c2 + -36c2 = 0 5 + 3c + -36c2 = 0 Factor a trinomial. (5 + -12c)(1 + 3c) = 0Subproblem 1
Set the factor '(5 + -12c)' equal to zero and attempt to solve: Simplifying 5 + -12c = 0 Solving 5 + -12c = 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 + -12c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12c = 0 + -5 -12c = 0 + -5 Combine like terms: 0 + -5 = -5 -12c = -5 Divide each side by '-12'. c = 0.4166666667 Simplifying c = 0.4166666667Subproblem 2
Set the factor '(1 + 3c)' equal to zero and attempt to solve: Simplifying 1 + 3c = 0 Solving 1 + 3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3c = 0 + -1 3c = 0 + -1 Combine like terms: 0 + -1 = -1 3c = -1 Divide each side by '3'. c = -0.3333333333 Simplifying c = -0.3333333333Solution
c = {0.4166666667, -0.3333333333}
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