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Simplifying (7k + -3)(2k + -7) = 0 Reorder the terms: (-3 + 7k)(2k + -7) = 0 Reorder the terms: (-3 + 7k)(-7 + 2k) = 0 Multiply (-3 + 7k) * (-7 + 2k) (-3(-7 + 2k) + 7k * (-7 + 2k)) = 0 ((-7 * -3 + 2k * -3) + 7k * (-7 + 2k)) = 0 ((21 + -6k) + 7k * (-7 + 2k)) = 0 (21 + -6k + (-7 * 7k + 2k * 7k)) = 0 (21 + -6k + (-49k + 14k2)) = 0 Combine like terms: -6k + -49k = -55k (21 + -55k + 14k2) = 0 Solving 21 + -55k + 14k2 = 0 Solving for variable 'k'. Factor a trinomial. (3 + -7k)(7 + -2k) = 0Subproblem 1
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 = 0.4285714286Subproblem 2
Set the factor '(7 + -2k)' equal to zero and attempt to solve: Simplifying 7 + -2k = 0 Solving 7 + -2k = 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 + -2k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2k = 0 + -7 -2k = 0 + -7 Combine like terms: 0 + -7 = -7 -2k = -7 Divide each side by '-2'. k = 3.5 Simplifying k = 3.5Solution
k = {0.4285714286, 3.5}
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