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Simplifying (2x + 1)(x + 2) + k = 0 Reorder the terms: (1 + 2x)(x + 2) + k = 0 Reorder the terms: (1 + 2x)(2 + x) + k = 0 Multiply (1 + 2x) * (2 + x) (1(2 + x) + 2x * (2 + x)) + k = 0 ((2 * 1 + x * 1) + 2x * (2 + x)) + k = 0 ((2 + 1x) + 2x * (2 + x)) + k = 0 (2 + 1x + (2 * 2x + x * 2x)) + k = 0 (2 + 1x + (4x + 2x2)) + k = 0 Combine like terms: 1x + 4x = 5x (2 + 5x + 2x2) + k = 0 Reorder the terms: 2 + k + 5x + 2x2 = 0 Solving 2 + k + 5x + 2x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + k + 5x + -2 + 2x2 = 0 + -2 Reorder the terms: 2 + -2 + k + 5x + 2x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k + 5x + 2x2 = 0 + -2 k + 5x + 2x2 = 0 + -2 Combine like terms: 0 + -2 = -2 k + 5x + 2x2 = -2 Add '-5x' to each side of the equation. k + 5x + -5x + 2x2 = -2 + -5x Combine like terms: 5x + -5x = 0 k + 0 + 2x2 = -2 + -5x k + 2x2 = -2 + -5x Add '-2x2' to each side of the equation. k + 2x2 + -2x2 = -2 + -5x + -2x2 Combine like terms: 2x2 + -2x2 = 0 k + 0 = -2 + -5x + -2x2 k = -2 + -5x + -2x2 Simplifying k = -2 + -5x + -2x2
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