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Simplifying (k + 4)(k + 7) = 0 Reorder the terms: (4 + k)(k + 7) = 0 Reorder the terms: (4 + k)(7 + k) = 0 Multiply (4 + k) * (7 + k) (4(7 + k) + k(7 + k)) = 0 ((7 * 4 + k * 4) + k(7 + k)) = 0 ((28 + 4k) + k(7 + k)) = 0 (28 + 4k + (7 * k + k * k)) = 0 (28 + 4k + (7k + k2)) = 0 Combine like terms: 4k + 7k = 11k (28 + 11k + k2) = 0 Solving 28 + 11k + k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + k)(4 + k) = 0Subproblem 1
Set the factor '(7 + k)' equal to zero and attempt to solve: Simplifying 7 + k = 0 Solving 7 + k = 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 + k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + k = 0 + -7 k = 0 + -7 Combine like terms: 0 + -7 = -7 k = -7 Simplifying k = -7Subproblem 2
Set the factor '(4 + k)' equal to zero and attempt to solve: Simplifying 4 + k = 0 Solving 4 + k = 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 + k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + k = 0 + -4 k = 0 + -4 Combine like terms: 0 + -4 = -4 k = -4 Simplifying k = -4Solution
k = {-7, -4}
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