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Simplifying [(k + 5) + -1(2k + -1)][(k + 5) + (2k + -1)] = 0 Reorder the terms: [(5 + k) + -1(2k + -1)][(k + 5) + (2k + -1)] = 0 Remove parenthesis around (5 + k) [5 + k + -1(2k + -1)][(k + 5) + (2k + -1)] = 0 Reorder the terms: [5 + k + -1(-1 + 2k)][(k + 5) + (2k + -1)] = 0 [5 + k + (-1 * -1 + 2k * -1)][(k + 5) + (2k + -1)] = 0 [5 + k + (1 + -2k)][(k + 5) + (2k + -1)] = 0 Reorder the terms: [5 + 1 + k + -2k][(k + 5) + (2k + -1)] = 0 Combine like terms: 5 + 1 = 6 [6 + k + -2k][(k + 5) + (2k + -1)] = 0 Combine like terms: k + -2k = -1k [6 + -1k][(k + 5) + (2k + -1)] = 0 Reorder the terms: [6 + -1k][(5 + k) + (2k + -1)] = 0 Remove parenthesis around (5 + k) [6 + -1k][5 + k + (2k + -1)] = 0 Reorder the terms: [6 + -1k][5 + k + (-1 + 2k)] = 0 Remove parenthesis around (-1 + 2k) [6 + -1k][5 + k + -1 + 2k] = 0 Reorder the terms: [6 + -1k][5 + -1 + k + 2k] = 0 Combine like terms: 5 + -1 = 4 [6 + -1k][4 + k + 2k] = 0 Combine like terms: k + 2k = 3k [6 + -1k][4 + 3k] = 0 Multiply [6 + -1k] * [4 + 3k] [6[4 + 3k] + -1k * [4 + 3k]] = 0 [[4 * 6 + 3k * 6] + -1k * [4 + 3k]] = 0 [[24 + 18k] + -1k * [4 + 3k]] = 0 [24 + 18k + [4 * -1k + 3k * -1k]] = 0 [24 + 18k + [-4k + -3k2]] = 0 Combine like terms: 18k + -4k = 14k [24 + 14k + -3k2] = 0 Solving 24 + 14k + -3k2 = 0 Solving for variable 'k'. Factor a trinomial. (6 + -1k)(4 + 3k) = 0Subproblem 1
Set the factor '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Subproblem 2
Set the factor '(4 + 3k)' equal to zero and attempt to solve: Simplifying 4 + 3k = 0 Solving 4 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3k = 0 + -4 3k = 0 + -4 Combine like terms: 0 + -4 = -4 3k = -4 Divide each side by '3'. k = -1.333333333 Simplifying k = -1.333333333Solution
k = {6, -1.333333333}
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