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Simplifying 2k(3k + -2) + -5(3k + -2) = 0 Reorder the terms: 2k(-2 + 3k) + -5(3k + -2) = 0 (-2 * 2k + 3k * 2k) + -5(3k + -2) = 0 (-4k + 6k2) + -5(3k + -2) = 0 Reorder the terms: -4k + 6k2 + -5(-2 + 3k) = 0 -4k + 6k2 + (-2 * -5 + 3k * -5) = 0 -4k + 6k2 + (10 + -15k) = 0 Reorder the terms: 10 + -4k + -15k + 6k2 = 0 Combine like terms: -4k + -15k = -19k 10 + -19k + 6k2 = 0 Solving 10 + -19k + 6k2 = 0 Solving for variable 'k'. Factor a trinomial. (2 + -3k)(5 + -2k) = 0Subproblem 1
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 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 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Subproblem 2
Set the factor '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 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 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5Solution
k = {0.6666666667, 2.5}
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