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Simplifying (2k + -3)(k + -4) = 0 Reorder the terms: (-3 + 2k)(k + -4) = 0 Reorder the terms: (-3 + 2k)(-4 + k) = 0 Multiply (-3 + 2k) * (-4 + k) (-3(-4 + k) + 2k * (-4 + k)) = 0 ((-4 * -3 + k * -3) + 2k * (-4 + k)) = 0 ((12 + -3k) + 2k * (-4 + k)) = 0 (12 + -3k + (-4 * 2k + k * 2k)) = 0 (12 + -3k + (-8k + 2k2)) = 0 Combine like terms: -3k + -8k = -11k (12 + -11k + 2k2) = 0 Solving 12 + -11k + 2k2 = 0 Solving for variable 'k'. Factor a trinomial. (3 + -2k)(4 + -1k) = 0Subproblem 1
Set the factor '(3 + -2k)' equal to zero and attempt to solve: Simplifying 3 + -2k = 0 Solving 3 + -2k = 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 + -2k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2k = 0 + -3 -2k = 0 + -3 Combine like terms: 0 + -3 = -3 -2k = -3 Divide each side by '-2'. k = 1.5 Simplifying k = 1.5Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {1.5, 4}
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