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Simplifying (2K + 4)(2K + 9) = 3K2 + 11K Reorder the terms: (4 + 2K)(2K + 9) = 3K2 + 11K Reorder the terms: (4 + 2K)(9 + 2K) = 3K2 + 11K Multiply (4 + 2K) * (9 + 2K) (4(9 + 2K) + 2K * (9 + 2K)) = 3K2 + 11K ((9 * 4 + 2K * 4) + 2K * (9 + 2K)) = 3K2 + 11K ((36 + 8K) + 2K * (9 + 2K)) = 3K2 + 11K (36 + 8K + (9 * 2K + 2K * 2K)) = 3K2 + 11K (36 + 8K + (18K + 4K2)) = 3K2 + 11K Combine like terms: 8K + 18K = 26K (36 + 26K + 4K2) = 3K2 + 11K Reorder the terms: 36 + 26K + 4K2 = 11K + 3K2 Solving 36 + 26K + 4K2 = 11K + 3K2 Solving for variable 'K'. Reorder the terms: 36 + 26K + -11K + 4K2 + -3K2 = 11K + 3K2 + -11K + -3K2 Combine like terms: 26K + -11K = 15K 36 + 15K + 4K2 + -3K2 = 11K + 3K2 + -11K + -3K2 Combine like terms: 4K2 + -3K2 = 1K2 36 + 15K + 1K2 = 11K + 3K2 + -11K + -3K2 Reorder the terms: 36 + 15K + 1K2 = 11K + -11K + 3K2 + -3K2 Combine like terms: 11K + -11K = 0 36 + 15K + 1K2 = 0 + 3K2 + -3K2 36 + 15K + 1K2 = 3K2 + -3K2 Combine like terms: 3K2 + -3K2 = 0 36 + 15K + 1K2 = 0 Factor a trinomial. (12 + K)(3 + K) = 0Subproblem 1
Set the factor '(12 + K)' equal to zero and attempt to solve: Simplifying 12 + K = 0 Solving 12 + K = 0 Move all terms containing K to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + K = 0 + -12 Combine like terms: 12 + -12 = 0 0 + K = 0 + -12 K = 0 + -12 Combine like terms: 0 + -12 = -12 K = -12 Simplifying K = -12Subproblem 2
Set the factor '(3 + K)' equal to zero and attempt to solve: Simplifying 3 + K = 0 Solving 3 + K = 0 Move all terms containing K to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + K = 0 + -3 Combine like terms: 3 + -3 = 0 0 + K = 0 + -3 K = 0 + -3 Combine like terms: 0 + -3 = -3 K = -3 Simplifying K = -3Solution
K = {-12, -3}
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