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Simplifying 15k3 + -114k2 = 189k Reorder the terms: -114k2 + 15k3 = 189k Solving -114k2 + 15k3 = 189k Solving for variable 'k'. Reorder the terms: -189k + -114k2 + 15k3 = 189k + -189k Combine like terms: 189k + -189k = 0 -189k + -114k2 + 15k3 = 0 Factor out the Greatest Common Factor (GCF), '3k'. 3k(-63 + -38k + 5k2) = 0 Factor a trinomial. 3k((-7 + -5k)(9 + -1k)) = 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 '(-7 + -5k)' equal to zero and attempt to solve: Simplifying -7 + -5k = 0 Solving -7 + -5k = 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 + -5k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5k = 0 + 7 -5k = 0 + 7 Combine like terms: 0 + 7 = 7 -5k = 7 Divide each side by '-5'. k = -1.4 Simplifying k = -1.4Subproblem 3
Set the factor '(9 + -1k)' equal to zero and attempt to solve: Simplifying 9 + -1k = 0 Solving 9 + -1k = 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 + -1k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1k = 0 + -9 -1k = 0 + -9 Combine like terms: 0 + -9 = -9 -1k = -9 Divide each side by '-1'. k = 9 Simplifying k = 9Solution
k = {0, -1.4, 9}
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