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Simplifying (4k + -3)(k + 7) = 0 Reorder the terms: (-3 + 4k)(k + 7) = 0 Reorder the terms: (-3 + 4k)(7 + k) = 0 Multiply (-3 + 4k) * (7 + k) (-3(7 + k) + 4k * (7 + k)) = 0 ((7 * -3 + k * -3) + 4k * (7 + k)) = 0 ((-21 + -3k) + 4k * (7 + k)) = 0 (-21 + -3k + (7 * 4k + k * 4k)) = 0 (-21 + -3k + (28k + 4k2)) = 0 Combine like terms: -3k + 28k = 25k (-21 + 25k + 4k2) = 0 Solving -21 + 25k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (-7 + -1k)(3 + -4k) = 0Subproblem 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 + -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 = {-7, 0.75}
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