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Simplifying (4k + -4)(8k + -7) = 0 Reorder the terms: (-4 + 4k)(8k + -7) = 0 Reorder the terms: (-4 + 4k)(-7 + 8k) = 0 Multiply (-4 + 4k) * (-7 + 8k) (-4(-7 + 8k) + 4k * (-7 + 8k)) = 0 ((-7 * -4 + 8k * -4) + 4k * (-7 + 8k)) = 0 ((28 + -32k) + 4k * (-7 + 8k)) = 0 (28 + -32k + (-7 * 4k + 8k * 4k)) = 0 (28 + -32k + (-28k + 32k2)) = 0 Combine like terms: -32k + -28k = -60k (28 + -60k + 32k2) = 0 Solving 28 + -60k + 32k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -15k + 8k2) = 0 Factor a trinomial. 4((7 + -8k)(1 + -1k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -8k)' equal to zero and attempt to solve: Simplifying 7 + -8k = 0 Solving 7 + -8k = 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 + -8k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8k = 0 + -7 -8k = 0 + -7 Combine like terms: 0 + -7 = -7 -8k = -7 Divide each side by '-8'. k = 0.875 Simplifying k = 0.875Subproblem 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 = {0.875, 1}
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