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Simplifying (3k + -2)(2k + -7) = 0 Reorder the terms: (-2 + 3k)(2k + -7) = 0 Reorder the terms: (-2 + 3k)(-7 + 2k) = 0 Multiply (-2 + 3k) * (-7 + 2k) (-2(-7 + 2k) + 3k * (-7 + 2k)) = 0 ((-7 * -2 + 2k * -2) + 3k * (-7 + 2k)) = 0 ((14 + -4k) + 3k * (-7 + 2k)) = 0 (14 + -4k + (-7 * 3k + 2k * 3k)) = 0 (14 + -4k + (-21k + 6k2)) = 0 Combine like terms: -4k + -21k = -25k (14 + -25k + 6k2) = 0 Solving 14 + -25k + 6k2 = 0 Solving for variable 'k'. Factor a trinomial. (2 + -3k)(7 + -2k) = 0Subproblem 1
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Subproblem 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 = {0.6666666667, 3.5}
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