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Simplifying 12k(k) + 15k = 16k + 20 Multiply k * k 12k2 + 15k = 16k + 20 Reorder the terms: 15k + 12k2 = 16k + 20 Reorder the terms: 15k + 12k2 = 20 + 16k Solving 15k + 12k2 = 20 + 16k Solving for variable 'k'. Reorder the terms: -20 + 15k + -16k + 12k2 = 20 + 16k + -20 + -16k Combine like terms: 15k + -16k = -1k -20 + -1k + 12k2 = 20 + 16k + -20 + -16k Reorder the terms: -20 + -1k + 12k2 = 20 + -20 + 16k + -16k Combine like terms: 20 + -20 = 0 -20 + -1k + 12k2 = 0 + 16k + -16k -20 + -1k + 12k2 = 16k + -16k Combine like terms: 16k + -16k = 0 -20 + -1k + 12k2 = 0 Factor a trinomial. (-5 + -4k)(4 + -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 '(4 + -3k)' equal to zero and attempt to solve: Simplifying 4 + -3k = 0 Solving 4 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3k = 0 + -4 -3k = 0 + -4 Combine like terms: 0 + -4 = -4 -3k = -4 Divide each side by '-3'. k = 1.333333333 Simplifying k = 1.333333333Solution
k = {-1.25, 1.333333333}
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