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Simplifying 3k(1 + 2k) + 2k(5k + -6) = 0 (1 * 3k + 2k * 3k) + 2k(5k + -6) = 0 (3k + 6k2) + 2k(5k + -6) = 0 Reorder the terms: 3k + 6k2 + 2k(-6 + 5k) = 0 3k + 6k2 + (-6 * 2k + 5k * 2k) = 0 3k + 6k2 + (-12k + 10k2) = 0 Reorder the terms: 3k + -12k + 6k2 + 10k2 = 0 Combine like terms: 3k + -12k = -9k -9k + 6k2 + 10k2 = 0 Combine like terms: 6k2 + 10k2 = 16k2 -9k + 16k2 = 0 Solving -9k + 16k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(-9 + 16k) = 0Subproblem 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 '(-9 + 16k)' equal to zero and attempt to solve: Simplifying -9 + 16k = 0 Solving -9 + 16k = 0 Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 16k = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16k = 0 + 9 16k = 0 + 9 Combine like terms: 0 + 9 = 9 16k = 9 Divide each side by '16'. k = 0.5625 Simplifying k = 0.5625Solution
k = {0, 0.5625}
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