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Simplifying (4k + 5)(3k + -2) = 0 Reorder the terms: (5 + 4k)(3k + -2) = 0 Reorder the terms: (5 + 4k)(-2 + 3k) = 0 Multiply (5 + 4k) * (-2 + 3k) (5(-2 + 3k) + 4k * (-2 + 3k)) = 0 ((-2 * 5 + 3k * 5) + 4k * (-2 + 3k)) = 0 ((-10 + 15k) + 4k * (-2 + 3k)) = 0 (-10 + 15k + (-2 * 4k + 3k * 4k)) = 0 (-10 + 15k + (-8k + 12k2)) = 0 Combine like terms: 15k + -8k = 7k (-10 + 7k + 12k2) = 0 Solving -10 + 7k + 12k2 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -4k)(2 + -3k) = 0Subproblem 1
Set the factor '(-5 + -4k)' equal to zero and attempt to solve: Simplifying -5 + -4k = 0 Solving -5 + -4k = 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 + -4k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4k = 0 + 5 -4k = 0 + 5 Combine like terms: 0 + 5 = 5 -4k = 5 Divide each side by '-4'. k = -1.25 Simplifying k = -1.25Subproblem 2
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 = 0.6666666667Solution
k = {-1.25, 0.6666666667}
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