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Simplifying (4k + 2)(k + -10) = 0 Reorder the terms: (2 + 4k)(k + -10) = 0 Reorder the terms: (2 + 4k)(-10 + k) = 0 Multiply (2 + 4k) * (-10 + k) (2(-10 + k) + 4k * (-10 + k)) = 0 ((-10 * 2 + k * 2) + 4k * (-10 + k)) = 0 ((-20 + 2k) + 4k * (-10 + k)) = 0 (-20 + 2k + (-10 * 4k + k * 4k)) = 0 (-20 + 2k + (-40k + 4k2)) = 0 Combine like terms: 2k + -40k = -38k (-20 + -38k + 4k2) = 0 Solving -20 + -38k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -19k + 2k2) = 0 Factor a trinomial. 2((-1 + -2k)(10 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2k)' equal to zero and attempt to solve: Simplifying -1 + -2k = 0 Solving -1 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2k = 0 + 1 -2k = 0 + 1 Combine like terms: 0 + 1 = 1 -2k = 1 Divide each side by '-2'. k = -0.5 Simplifying k = -0.5Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve: Simplifying 10 + -1k = 0 Solving 10 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1k = 0 + -10 -1k = 0 + -10 Combine like terms: 0 + -10 = -10 -1k = -10 Divide each side by '-1'. k = 10 Simplifying k = 10Solution
k = {-0.5, 10}
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