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Simplifying (5k + 3)(3k + -3) = 0 Reorder the terms: (3 + 5k)(3k + -3) = 0 Reorder the terms: (3 + 5k)(-3 + 3k) = 0 Multiply (3 + 5k) * (-3 + 3k) (3(-3 + 3k) + 5k * (-3 + 3k)) = 0 ((-3 * 3 + 3k * 3) + 5k * (-3 + 3k)) = 0 ((-9 + 9k) + 5k * (-3 + 3k)) = 0 (-9 + 9k + (-3 * 5k + 3k * 5k)) = 0 (-9 + 9k + (-15k + 15k2)) = 0 Combine like terms: 9k + -15k = -6k (-9 + -6k + 15k2) = 0 Solving -9 + -6k + 15k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -2k + 5k2) = 0 Factor a trinomial. 3((-3 + -5k)(1 + -1k)) = 0 Ignore the factor 3.Subproblem 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 '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Solution
k = {-0.6, 1}
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