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Simplifying (k + 2)(3k + -5) = 0 Reorder the terms: (2 + k)(3k + -5) = 0 Reorder the terms: (2 + k)(-5 + 3k) = 0 Multiply (2 + k) * (-5 + 3k) (2(-5 + 3k) + k(-5 + 3k)) = 0 ((-5 * 2 + 3k * 2) + k(-5 + 3k)) = 0 ((-10 + 6k) + k(-5 + 3k)) = 0 (-10 + 6k + (-5 * k + 3k * k)) = 0 (-10 + 6k + (-5k + 3k2)) = 0 Combine like terms: 6k + -5k = 1k (-10 + 1k + 3k2) = 0 Solving -10 + 1k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (-2 + -1k)(5 + -3k) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667Solution
k = {-2, 1.666666667}
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