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Simplifying (x + -3)(2x + 5) = x + -15 + k Reorder the terms: (-3 + x)(2x + 5) = x + -15 + k Reorder the terms: (-3 + x)(5 + 2x) = x + -15 + k Multiply (-3 + x) * (5 + 2x) (-3(5 + 2x) + x(5 + 2x)) = x + -15 + k ((5 * -3 + 2x * -3) + x(5 + 2x)) = x + -15 + k ((-15 + -6x) + x(5 + 2x)) = x + -15 + k (-15 + -6x + (5 * x + 2x * x)) = x + -15 + k (-15 + -6x + (5x + 2x2)) = x + -15 + k Combine like terms: -6x + 5x = -1x (-15 + -1x + 2x2) = x + -15 + k Reorder the terms: -15 + -1x + 2x2 = -15 + k + x Add '15' to each side of the equation. -15 + -1x + 15 + 2x2 = -15 + k + 15 + x Reorder the terms: -15 + 15 + -1x + 2x2 = -15 + k + 15 + x Combine like terms: -15 + 15 = 0 0 + -1x + 2x2 = -15 + k + 15 + x -1x + 2x2 = -15 + k + 15 + x Reorder the terms: -1x + 2x2 = -15 + 15 + k + x Combine like terms: -15 + 15 = 0 -1x + 2x2 = 0 + k + x -1x + 2x2 = k + x Solving -1x + 2x2 = k + x Solving for variable 'x'. Reorder the terms: -1k + -1x + -1x + 2x2 = k + x + -1k + -1x Combine like terms: -1x + -1x = -2x -1k + -2x + 2x2 = k + x + -1k + -1x Reorder the terms: -1k + -2x + 2x2 = k + -1k + x + -1x Combine like terms: k + -1k = 0 -1k + -2x + 2x2 = 0 + x + -1x -1k + -2x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -1k + -2x + 2x2 = 0 The solution to this equation could not be determined.
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