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Simplifying (5k + 4)(3k + -4) = 0 Reorder the terms: (4 + 5k)(3k + -4) = 0 Reorder the terms: (4 + 5k)(-4 + 3k) = 0 Multiply (4 + 5k) * (-4 + 3k) (4(-4 + 3k) + 5k * (-4 + 3k)) = 0 ((-4 * 4 + 3k * 4) + 5k * (-4 + 3k)) = 0 ((-16 + 12k) + 5k * (-4 + 3k)) = 0 (-16 + 12k + (-4 * 5k + 3k * 5k)) = 0 (-16 + 12k + (-20k + 15k2)) = 0 Combine like terms: 12k + -20k = -8k (-16 + -8k + 15k2) = 0 Solving -16 + -8k + 15k2 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -5k)(4 + -3k) = 0Subproblem 1
Set the factor '(-4 + -5k)' equal to zero and attempt to solve: Simplifying -4 + -5k = 0 Solving -4 + -5k = 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 + -5k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5k = 0 + 4 -5k = 0 + 4 Combine like terms: 0 + 4 = 4 -5k = 4 Divide each side by '-5'. k = -0.8 Simplifying k = -0.8Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve: Simplifying 4 + -3k = 0 Solving 4 + -3k = 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 + -3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3k = 0 + -4 -3k = 0 + -4 Combine like terms: 0 + -4 = -4 -3k = -4 Divide each side by '-3'. k = 1.333333333 Simplifying k = 1.333333333Solution
k = {-0.8, 1.333333333}
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