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Simplifying 2k(3k + 4) + -19 = k(6k + -2) + 31 Reorder the terms: 2k(4 + 3k) + -19 = k(6k + -2) + 31 (4 * 2k + 3k * 2k) + -19 = k(6k + -2) + 31 (8k + 6k2) + -19 = k(6k + -2) + 31 Reorder the terms: -19 + 8k + 6k2 = k(6k + -2) + 31 Reorder the terms: -19 + 8k + 6k2 = k(-2 + 6k) + 31 -19 + 8k + 6k2 = (-2 * k + 6k * k) + 31 -19 + 8k + 6k2 = (-2k + 6k2) + 31 Reorder the terms: -19 + 8k + 6k2 = 31 + -2k + 6k2 Add '-6k2' to each side of the equation. -19 + 8k + 6k2 + -6k2 = 31 + -2k + 6k2 + -6k2 Combine like terms: 6k2 + -6k2 = 0 -19 + 8k + 0 = 31 + -2k + 6k2 + -6k2 -19 + 8k = 31 + -2k + 6k2 + -6k2 Combine like terms: 6k2 + -6k2 = 0 -19 + 8k = 31 + -2k + 0 -19 + 8k = 31 + -2k Solving -19 + 8k = 31 + -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. -19 + 8k + 2k = 31 + -2k + 2k Combine like terms: 8k + 2k = 10k -19 + 10k = 31 + -2k + 2k Combine like terms: -2k + 2k = 0 -19 + 10k = 31 + 0 -19 + 10k = 31 Add '19' to each side of the equation. -19 + 19 + 10k = 31 + 19 Combine like terms: -19 + 19 = 0 0 + 10k = 31 + 19 10k = 31 + 19 Combine like terms: 31 + 19 = 50 10k = 50 Divide each side by '10'. k = 5 Simplifying k = 5
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