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Simplifying 5(k2 + k + 3) + -1k2 = 2(2k2 + 4k + 7) + -5 Reorder the terms: 5(3 + k + k2) + -1k2 = 2(2k2 + 4k + 7) + -5 (3 * 5 + k * 5 + k2 * 5) + -1k2 = 2(2k2 + 4k + 7) + -5 (15 + 5k + 5k2) + -1k2 = 2(2k2 + 4k + 7) + -5 Combine like terms: 5k2 + -1k2 = 4k2 15 + 5k + 4k2 = 2(2k2 + 4k + 7) + -5 Reorder the terms: 15 + 5k + 4k2 = 2(7 + 4k + 2k2) + -5 15 + 5k + 4k2 = (7 * 2 + 4k * 2 + 2k2 * 2) + -5 15 + 5k + 4k2 = (14 + 8k + 4k2) + -5 Reorder the terms: 15 + 5k + 4k2 = 14 + -5 + 8k + 4k2 Combine like terms: 14 + -5 = 9 15 + 5k + 4k2 = 9 + 8k + 4k2 Add '-4k2' to each side of the equation. 15 + 5k + 4k2 + -4k2 = 9 + 8k + 4k2 + -4k2 Combine like terms: 4k2 + -4k2 = 0 15 + 5k + 0 = 9 + 8k + 4k2 + -4k2 15 + 5k = 9 + 8k + 4k2 + -4k2 Combine like terms: 4k2 + -4k2 = 0 15 + 5k = 9 + 8k + 0 15 + 5k = 9 + 8k Solving 15 + 5k = 9 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 15 + 5k + -8k = 9 + 8k + -8k Combine like terms: 5k + -8k = -3k 15 + -3k = 9 + 8k + -8k Combine like terms: 8k + -8k = 0 15 + -3k = 9 + 0 15 + -3k = 9 Add '-15' to each side of the equation. 15 + -15 + -3k = 9 + -15 Combine like terms: 15 + -15 = 0 0 + -3k = 9 + -15 -3k = 9 + -15 Combine like terms: 9 + -15 = -6 -3k = -6 Divide each side by '-3'. k = 2 Simplifying k = 2
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