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Simplifying (8k + -1)(4k + -3) = 0 Reorder the terms: (-1 + 8k)(4k + -3) = 0 Reorder the terms: (-1 + 8k)(-3 + 4k) = 0 Multiply (-1 + 8k) * (-3 + 4k) (-1(-3 + 4k) + 8k * (-3 + 4k)) = 0 ((-3 * -1 + 4k * -1) + 8k * (-3 + 4k)) = 0 ((3 + -4k) + 8k * (-3 + 4k)) = 0 (3 + -4k + (-3 * 8k + 4k * 8k)) = 0 (3 + -4k + (-24k + 32k2)) = 0 Combine like terms: -4k + -24k = -28k (3 + -28k + 32k2) = 0 Solving 3 + -28k + 32k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -8k)(3 + -4k) = 0Subproblem 1
Set the factor '(1 + -8k)' equal to zero and attempt to solve: Simplifying 1 + -8k = 0 Solving 1 + -8k = 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 + -8k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8k = 0 + -1 -8k = 0 + -1 Combine like terms: 0 + -1 = -1 -8k = -1 Divide each side by '-8'. k = 0.125 Simplifying k = 0.125Subproblem 2
Set the factor '(3 + -4k)' equal to zero and attempt to solve: Simplifying 3 + -4k = 0 Solving 3 + -4k = 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 + -4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4k = 0 + -3 -4k = 0 + -3 Combine like terms: 0 + -3 = -3 -4k = -3 Divide each side by '-4'. k = 0.75 Simplifying k = 0.75Solution
k = {0.125, 0.75}
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