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Simplifying [4 + -1(3c + -1)][6 + -1(3c + -1)] = 0 Reorder the terms: [4 + -1(-1 + 3c)][6 + -1(3c + -1)] = 0 [4 + (-1 * -1 + 3c * -1)][6 + -1(3c + -1)] = 0 [4 + (1 + -3c)][6 + -1(3c + -1)] = 0 Combine like terms: 4 + 1 = 5 [5 + -3c][6 + -1(3c + -1)] = 0 Reorder the terms: [5 + -3c][6 + -1(-1 + 3c)] = 0 [5 + -3c][6 + (-1 * -1 + 3c * -1)] = 0 [5 + -3c][6 + (1 + -3c)] = 0 Combine like terms: 6 + 1 = 7 [5 + -3c][7 + -3c] = 0 Multiply [5 + -3c] * [7 + -3c] [5[7 + -3c] + -3c * [7 + -3c]] = 0 [[7 * 5 + -3c * 5] + -3c * [7 + -3c]] = 0 [[35 + -15c] + -3c * [7 + -3c]] = 0 [35 + -15c + [7 * -3c + -3c * -3c]] = 0 [35 + -15c + [-21c + 9c2]] = 0 Combine like terms: -15c + -21c = -36c [35 + -36c + 9c2] = 0 Solving 35 + -36c + 9c2 = 0 Solving for variable 'c'. Factor a trinomial. (5 + -3c)(7 + -3c) = 0Subproblem 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 '(7 + -3c)' equal to zero and attempt to solve: Simplifying 7 + -3c = 0 Solving 7 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3c = 0 + -7 -3c = 0 + -7 Combine like terms: 0 + -7 = -7 -3c = -7 Divide each side by '-3'. c = 2.333333333 Simplifying c = 2.333333333Solution
c = {1.666666667, 2.333333333}
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