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Simplifying -5K(2 + K)(3 + -6K) = 0 Multiply (2 + K) * (3 + -6K) -5K(2(3 + -6K) + K(3 + -6K)) = 0 -5K((3 * 2 + -6K * 2) + K(3 + -6K)) = 0 -5K((6 + -12K) + K(3 + -6K)) = 0 -5K(6 + -12K + (3 * K + -6K * K)) = 0 -5K(6 + -12K + (3K + -6K2)) = 0 Combine like terms: -12K + 3K = -9K -5K(6 + -9K + -6K2) = 0 (6 * -5K + -9K * -5K + -6K2 * -5K) = 0 (-30K + 45K2 + 30K3) = 0 Solving -30K + 45K2 + 30K3 = 0 Solving for variable 'K'. Factor out the Greatest Common Factor (GCF), '15K'. 15K(-2 + 3K + 2K2) = 0 Factor a trinomial. 15K((-2 + -1K)(1 + -2K)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'K' equal to zero and attempt to solve: Simplifying K = 0 Solving K = 0 Move all terms containing K to the left, all other terms to the right. Simplifying K = 0Subproblem 2
Set the factor '(-2 + -1K)' equal to zero and attempt to solve: Simplifying -2 + -1K = 0 Solving -2 + -1K = 0 Move all terms containing K to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1K = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1K = 0 + 2 -1K = 0 + 2 Combine like terms: 0 + 2 = 2 -1K = 2 Divide each side by '-1'. K = -2 Simplifying K = -2Subproblem 3
Set the factor '(1 + -2K)' equal to zero and attempt to solve: Simplifying 1 + -2K = 0 Solving 1 + -2K = 0 Move all terms containing K to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2K = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2K = 0 + -1 -2K = 0 + -1 Combine like terms: 0 + -1 = -1 -2K = -1 Divide each side by '-2'. K = 0.5 Simplifying K = 0.5Solution
K = {0, -2, 0.5}
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