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Simplifying -3(k + -7)(8k + 3) = 0 Reorder the terms: -3(-7 + k)(8k + 3) = 0 Reorder the terms: -3(-7 + k)(3 + 8k) = 0 Multiply (-7 + k) * (3 + 8k) -3(-7(3 + 8k) + k(3 + 8k)) = 0 -3((3 * -7 + 8k * -7) + k(3 + 8k)) = 0 -3((-21 + -56k) + k(3 + 8k)) = 0 -3(-21 + -56k + (3 * k + 8k * k)) = 0 -3(-21 + -56k + (3k + 8k2)) = 0 Combine like terms: -56k + 3k = -53k -3(-21 + -53k + 8k2) = 0 (-21 * -3 + -53k * -3 + 8k2 * -3) = 0 (63 + 159k + -24k2) = 0 Solving 63 + 159k + -24k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + 53k + -8k2) = 0 Factor a trinomial. 3((7 + -1k)(3 + 8k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Subproblem 2
Set the factor '(3 + 8k)' equal to zero and attempt to solve: Simplifying 3 + 8k = 0 Solving 3 + 8k = 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 + 8k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8k = 0 + -3 8k = 0 + -3 Combine like terms: 0 + -3 = -3 8k = -3 Divide each side by '8'. k = -0.375 Simplifying k = -0.375Solution
k = {7, -0.375}
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