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Simplifying (2x + 3)(x + k) = 0 Reorder the terms: (3 + 2x)(x + k) = 0 Reorder the terms: (3 + 2x)(k + x) = 0 Multiply (3 + 2x) * (k + x) (3(k + x) + 2x * (k + x)) = 0 ((k * 3 + x * 3) + 2x * (k + x)) = 0 ((3k + 3x) + 2x * (k + x)) = 0 (3k + 3x + (k * 2x + x * 2x)) = 0 (3k + 3x + (2kx + 2x2)) = 0 Reorder the terms: (3k + 2kx + 3x + 2x2) = 0 (3k + 2kx + 3x + 2x2) = 0 Solving 3k + 2kx + 3x + 2x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3x' to each side of the equation. 3k + 2kx + 3x + -3x + 2x2 = 0 + -3x Combine like terms: 3x + -3x = 0 3k + 2kx + 0 + 2x2 = 0 + -3x 3k + 2kx + 2x2 = 0 + -3x Remove the zero: 3k + 2kx + 2x2 = -3x Add '-2x2' to each side of the equation. 3k + 2kx + 2x2 + -2x2 = -3x + -2x2 Combine like terms: 2x2 + -2x2 = 0 3k + 2kx + 0 = -3x + -2x2 3k + 2kx = -3x + -2x2 Reorder the terms: 3k + 2kx + 3x + 2x2 = -3x + 3x + -2x2 + 2x2 Combine like terms: -3x + 3x = 0 3k + 2kx + 3x + 2x2 = 0 + -2x2 + 2x2 3k + 2kx + 3x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 3k + 2kx + 3x + 2x2 = 0 The solution to this equation could not be determined.
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