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Simplifying 6k3 + -19k2 + -7k = 0 Reorder the terms: -7k + -19k2 + 6k3 = 0 Solving -7k + -19k2 + 6k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(-7 + -19k + 6k2) = 0 Factor a trinomial. k((-1 + -3k)(7 + -2k)) = 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 '(-1 + -3k)' equal to zero and attempt to solve: Simplifying -1 + -3k = 0 Solving -1 + -3k = 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 + -3k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3k = 0 + 1 -3k = 0 + 1 Combine like terms: 0 + 1 = 1 -3k = 1 Divide each side by '-3'. k = -0.3333333333 Simplifying k = -0.3333333333Subproblem 3
Set the factor '(7 + -2k)' equal to zero and attempt to solve: Simplifying 7 + -2k = 0 Solving 7 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2k = 0 + -7 -2k = 0 + -7 Combine like terms: 0 + -7 = -7 -2k = -7 Divide each side by '-2'. k = 3.5 Simplifying k = 3.5Solution
k = {0, -0.3333333333, 3.5}
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