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Simplifying (2k + -7)(-3k + 5) = 0 Reorder the terms: (-7 + 2k)(-3k + 5) = 0 Reorder the terms: (-7 + 2k)(5 + -3k) = 0 Multiply (-7 + 2k) * (5 + -3k) (-7(5 + -3k) + 2k * (5 + -3k)) = 0 ((5 * -7 + -3k * -7) + 2k * (5 + -3k)) = 0 ((-35 + 21k) + 2k * (5 + -3k)) = 0 (-35 + 21k + (5 * 2k + -3k * 2k)) = 0 (-35 + 21k + (10k + -6k2)) = 0 Combine like terms: 21k + 10k = 31k (-35 + 31k + -6k2) = 0 Solving -35 + 31k + -6k2 = 0 Solving for variable 'k'. Factor a trinomial. (-7 + 2k)(5 + -3k) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667Solution
k = {3.5, 1.666666667}
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