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