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Simplifying (7k + 8)(-9k2 + -5k) = 0 Reorder the terms: (8 + 7k)(-9k2 + -5k) = 0 Reorder the terms: (8 + 7k)(-5k + -9k2) = 0 Multiply (8 + 7k) * (-5k + -9k2) (8(-5k + -9k2) + 7k * (-5k + -9k2)) = 0 ((-5k * 8 + -9k2 * 8) + 7k * (-5k + -9k2)) = 0 ((-40k + -72k2) + 7k * (-5k + -9k2)) = 0 (-40k + -72k2 + (-5k * 7k + -9k2 * 7k)) = 0 (-40k + -72k2 + (-35k2 + -63k3)) = 0 Combine like terms: -72k2 + -35k2 = -107k2 (-40k + -107k2 + -63k3) = 0 Solving -40k + -107k2 + -63k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1k'. -1k(40 + 107k + 63k2) = 0 Factor a trinomial. -1k((8 + 7k)(5 + 9k)) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(8 + 7k)' equal to zero and attempt to solve: Simplifying 8 + 7k = 0 Solving 8 + 7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7k = 0 + -8 7k = 0 + -8 Combine like terms: 0 + -8 = -8 7k = -8 Divide each side by '7'. k = -1.142857143 Simplifying k = -1.142857143Subproblem 3
Set the factor '(5 + 9k)' equal to zero and attempt to solve: Simplifying 5 + 9k = 0 Solving 5 + 9k = 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 + 9k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9k = 0 + -5 9k = 0 + -5 Combine like terms: 0 + -5 = -5 9k = -5 Divide each side by '9'. k = -0.5555555556 Simplifying k = -0.5555555556Solution
k = {0, -1.142857143, -0.5555555556}
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