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Simplifying (12 + k) * k = (k + 4)(K + 4) Reorder the terms for easier multiplication: k(12 + k) = (k + 4)(K + 4) (12 * k + k * k) = (k + 4)(K + 4) (12k + k2) = (k + 4)(K + 4) Reorder the terms: 12k + k2 = (4 + k)(K + 4) Reorder the terms: 12k + k2 = (4 + k)(4 + K) Multiply (4 + k) * (4 + K) 12k + k2 = (4(4 + K) + k(4 + K)) 12k + k2 = ((4 * 4 + K * 4) + k(4 + K)) 12k + k2 = ((16 + 4K) + k(4 + K)) 12k + k2 = (16 + 4K + (4 * k + K * k)) 12k + k2 = (16 + 4K + (4k + kK)) 12k + k2 = (16 + 4K + 4k + kK) Solving 12k + k2 = 16 + 4K + 4k + kK Solving for variable 'k'. Reorder the terms: -16 + -4K + 12k + -4k + -1kK + k2 = 16 + 4K + 4k + kK + -16 + -4K + -4k + -1kK Combine like terms: 12k + -4k = 8k -16 + -4K + 8k + -1kK + k2 = 16 + 4K + 4k + kK + -16 + -4K + -4k + -1kK Reorder the terms: -16 + -4K + 8k + -1kK + k2 = 16 + -16 + 4K + -4K + 4k + -4k + kK + -1kK Combine like terms: 16 + -16 = 0 -16 + -4K + 8k + -1kK + k2 = 0 + 4K + -4K + 4k + -4k + kK + -1kK -16 + -4K + 8k + -1kK + k2 = 4K + -4K + 4k + -4k + kK + -1kK Combine like terms: 4K + -4K = 0 -16 + -4K + 8k + -1kK + k2 = 0 + 4k + -4k + kK + -1kK -16 + -4K + 8k + -1kK + k2 = 4k + -4k + kK + -1kK Combine like terms: 4k + -4k = 0 -16 + -4K + 8k + -1kK + k2 = 0 + kK + -1kK -16 + -4K + 8k + -1kK + k2 = kK + -1kK Combine like terms: kK + -1kK = 0 -16 + -4K + 8k + -1kK + k2 = 0 The solution to this equation could not be determined.
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