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Simplifying 5k(3k + -3) + 6k(1 + -6k) = 0 Reorder the terms: 5k(-3 + 3k) + 6k(1 + -6k) = 0 (-3 * 5k + 3k * 5k) + 6k(1 + -6k) = 0 (-15k + 15k2) + 6k(1 + -6k) = 0 -15k + 15k2 + (1 * 6k + -6k * 6k) = 0 -15k + 15k2 + (6k + -36k2) = 0 Reorder the terms: -15k + 6k + 15k2 + -36k2 = 0 Combine like terms: -15k + 6k = -9k -9k + 15k2 + -36k2 = 0 Combine like terms: 15k2 + -36k2 = -21k2 -9k + -21k2 = 0 Solving -9k + -21k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-3k'. -3k(3 + 7k) = 0 Ignore the factor -3.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 '(3 + 7k)' equal to zero and attempt to solve: Simplifying 3 + 7k = 0 Solving 3 + 7k = 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 + 7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7k = 0 + -3 7k = 0 + -3 Combine like terms: 0 + -3 = -3 7k = -3 Divide each side by '7'. k = -0.4285714286 Simplifying k = -0.4285714286Solution
k = {0, -0.4285714286}
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