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Simplifying -2((k + -1)(-3) + -12) + -1(-1(-4)) = -1(4 + -2K) Reorder the terms: -2((-1 + k)(-3) + -12) + -1(-1(-4)) = -1(4 + -2K) Reorder the terms for easier multiplication: -2(-3(-1 + k) + -12) + -1(-1(-4)) = -1(4 + -2K) -2((-1 * -3 + k * -3) + -12) + -1(-1(-4)) = -1(4 + -2K) -2((3 + -3k) + -12) + -1(-1(-4)) = -1(4 + -2K) Reorder the terms: -2(3 + -12 + -3k) + -1(-1(-4)) = -1(4 + -2K) Combine like terms: 3 + -12 = -9 -2(-9 + -3k) + -1(-1(-4)) = -1(4 + -2K) (-9 * -2 + -3k * -2) + -1(-1(-4)) = -1(4 + -2K) (18 + 6k) + -1(-1(-4)) = -1(4 + -2K) Multiply -1 * -4 18 + 6k + -1(4) = -1(4 + -2K) Multiply -1 * 4 18 + 6k + -4 = -1(4 + -2K) Reorder the terms: 18 + -4 + 6k = -1(4 + -2K) Combine like terms: 18 + -4 = 14 14 + 6k = -1(4 + -2K) 14 + 6k = (4 * -1 + -2K * -1) 14 + 6k = (-4 + 2K) Solving 14 + 6k = -4 + 2K Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 6k = -4 + -14 + 2K Combine like terms: 14 + -14 = 0 0 + 6k = -4 + -14 + 2K 6k = -4 + -14 + 2K Combine like terms: -4 + -14 = -18 6k = -18 + 2K Divide each side by '6'. k = -3 + 0.3333333333K Simplifying k = -3 + 0.3333333333K
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