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Simplifying (k + 5)(2k + -3) = 2k2 + -1 Reorder the terms: (5 + k)(2k + -3) = 2k2 + -1 Reorder the terms: (5 + k)(-3 + 2k) = 2k2 + -1 Multiply (5 + k) * (-3 + 2k) (5(-3 + 2k) + k(-3 + 2k)) = 2k2 + -1 ((-3 * 5 + 2k * 5) + k(-3 + 2k)) = 2k2 + -1 ((-15 + 10k) + k(-3 + 2k)) = 2k2 + -1 (-15 + 10k + (-3 * k + 2k * k)) = 2k2 + -1 (-15 + 10k + (-3k + 2k2)) = 2k2 + -1 Combine like terms: 10k + -3k = 7k (-15 + 7k + 2k2) = 2k2 + -1 Reorder the terms: -15 + 7k + 2k2 = -1 + 2k2 Add '-2k2' to each side of the equation. -15 + 7k + 2k2 + -2k2 = -1 + 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -15 + 7k + 0 = -1 + 2k2 + -2k2 -15 + 7k = -1 + 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -15 + 7k = -1 + 0 -15 + 7k = -1 Solving -15 + 7k = -1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 7k = -1 + 15 Combine like terms: -15 + 15 = 0 0 + 7k = -1 + 15 7k = -1 + 15 Combine like terms: -1 + 15 = 14 7k = 14 Divide each side by '7'. k = 2 Simplifying k = 2
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