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Simplifying 2k(-3k + 4) + 6(10 + (k2)) = k(4k + 8) + -2k(2k + 5) Reorder the terms: 2k(4 + -3k) + 6(10 + (k2)) = k(4k + 8) + -2k(2k + 5) (4 * 2k + -3k * 2k) + 6(10 + (k2)) = k(4k + 8) + -2k(2k + 5) (8k + -6k2) + 6(10 + (k2)) = k(4k + 8) + -2k(2k + 5) 8k + -6k2 + 6(10 + k2) = k(4k + 8) + -2k(2k + 5) 8k + -6k2 + (10 * 6 + k2 * 6) = k(4k + 8) + -2k(2k + 5) 8k + -6k2 + (60 + 6k2) = k(4k + 8) + -2k(2k + 5) Reorder the terms: 60 + 8k + -6k2 + 6k2 = k(4k + 8) + -2k(2k + 5) Combine like terms: -6k2 + 6k2 = 0 60 + 8k + 0 = k(4k + 8) + -2k(2k + 5) 60 + 8k = k(4k + 8) + -2k(2k + 5) Reorder the terms: 60 + 8k = k(8 + 4k) + -2k(2k + 5) 60 + 8k = (8 * k + 4k * k) + -2k(2k + 5) 60 + 8k = (8k + 4k2) + -2k(2k + 5) Reorder the terms: 60 + 8k = 8k + 4k2 + -2k(5 + 2k) 60 + 8k = 8k + 4k2 + (5 * -2k + 2k * -2k) 60 + 8k = 8k + 4k2 + (-10k + -4k2) Reorder the terms: 60 + 8k = 8k + -10k + 4k2 + -4k2 Combine like terms: 8k + -10k = -2k 60 + 8k = -2k + 4k2 + -4k2 Combine like terms: 4k2 + -4k2 = 0 60 + 8k = -2k + 0 60 + 8k = -2k Solving 60 + 8k = -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. 60 + 8k + 2k = -2k + 2k Combine like terms: 8k + 2k = 10k 60 + 10k = -2k + 2k Combine like terms: -2k + 2k = 0 60 + 10k = 0 Add '-60' to each side of the equation. 60 + -60 + 10k = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 10k = 0 + -60 10k = 0 + -60 Combine like terms: 0 + -60 = -60 10k = -60 Divide each side by '10'. k = -6 Simplifying k = -6
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