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Simplifying (5k + 3)(k + -2) = 0 Reorder the terms: (3 + 5k)(k + -2) = 0 Reorder the terms: (3 + 5k)(-2 + k) = 0 Multiply (3 + 5k) * (-2 + k) (3(-2 + k) + 5k * (-2 + k)) = 0 ((-2 * 3 + k * 3) + 5k * (-2 + k)) = 0 ((-6 + 3k) + 5k * (-2 + k)) = 0 (-6 + 3k + (-2 * 5k + k * 5k)) = 0 (-6 + 3k + (-10k + 5k2)) = 0 Combine like terms: 3k + -10k = -7k (-6 + -7k + 5k2) = 0 Solving -6 + -7k + 5k2 = 0 Solving for variable 'k'. Factor a trinomial. (-3 + -5k)(2 + -1k) = 0Subproblem 1
Set the factor '(-3 + -5k)' equal to zero and attempt to solve: Simplifying -3 + -5k = 0 Solving -3 + -5k = 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 + -5k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5k = 0 + 3 -5k = 0 + 3 Combine like terms: 0 + 3 = 3 -5k = 3 Divide each side by '-5'. k = -0.6 Simplifying k = -0.6Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {-0.6, 2}
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