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Simplifying -4k(-6 + 6k) + k(-9 + k) = 0 (-6 * -4k + 6k * -4k) + k(-9 + k) = 0 (24k + -24k2) + k(-9 + k) = 0 24k + -24k2 + (-9 * k + k * k) = 0 24k + -24k2 + (-9k + k2) = 0 Reorder the terms: 24k + -9k + -24k2 + k2 = 0 Combine like terms: 24k + -9k = 15k 15k + -24k2 + k2 = 0 Combine like terms: -24k2 + k2 = -23k2 15k + -23k2 = 0 Solving 15k + -23k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(15 + -23k) = 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 '(15 + -23k)' equal to zero and attempt to solve: Simplifying 15 + -23k = 0 Solving 15 + -23k = 0 Move all terms containing k to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -23k = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -23k = 0 + -15 -23k = 0 + -15 Combine like terms: 0 + -15 = -15 -23k = -15 Divide each side by '-23'. k = 0.652173913 Simplifying k = 0.652173913Solution
k = {0, 0.652173913}
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