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Simplifying (7k + -3)(k + -2k + 7) = 0 Reorder the terms: (-3 + 7k)(k + -2k + 7) = 0 Reorder the terms: (-3 + 7k)(7 + k + -2k) = 0 Combine like terms: k + -2k = -1k (-3 + 7k)(7 + -1k) = 0 Multiply (-3 + 7k) * (7 + -1k) (-3(7 + -1k) + 7k * (7 + -1k)) = 0 ((7 * -3 + -1k * -3) + 7k * (7 + -1k)) = 0 ((-21 + 3k) + 7k * (7 + -1k)) = 0 (-21 + 3k + (7 * 7k + -1k * 7k)) = 0 (-21 + 3k + (49k + -7k2)) = 0 Combine like terms: 3k + 49k = 52k (-21 + 52k + -7k2) = 0 Solving -21 + 52k + -7k2 = 0 Solving for variable 'k'. Factor a trinomial. (-7 + k)(3 + -7k) = 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 '(3 + -7k)' equal to zero and attempt to solve: Simplifying 3 + -7k = 0 Solving 3 + -7k = 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 + -7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7k = 0 + -3 -7k = 0 + -3 Combine like terms: 0 + -3 = -3 -7k = -3 Divide each side by '-7'. k = 0.4285714286 Simplifying k = 0.4285714286Solution
k = {7, 0.4285714286}
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