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Simplifying k(x + -1) * 2 = kx + -1 + (x + -1)(x + 1) * k Reorder the terms: k(-1 + x) * 2 = kx + -1 + (x + -1)(x + 1) * k Reorder the terms for easier multiplication: 2k(-1 + x) = kx + -1 + (x + -1)(x + 1) * k (-1 * 2k + x * 2k) = kx + -1 + (x + -1)(x + 1) * k (-2k + 2kx) = kx + -1 + (x + -1)(x + 1) * k Reorder the terms: -2k + 2kx = kx + -1 + (-1 + x)(x + 1) * k Reorder the terms: -2k + 2kx = kx + -1 + (-1 + x)(1 + x) * k Reorder the terms for easier multiplication: -2k + 2kx = kx + -1 + k(-1 + x)(1 + x) Multiply (-1 + x) * (1 + x) -2k + 2kx = kx + -1 + k(-1(1 + x) + x(1 + x)) -2k + 2kx = kx + -1 + k((1 * -1 + x * -1) + x(1 + x)) -2k + 2kx = kx + -1 + k((-1 + -1x) + x(1 + x)) -2k + 2kx = kx + -1 + k(-1 + -1x + (1 * x + x * x)) -2k + 2kx = kx + -1 + k(-1 + -1x + (1x + x2)) Combine like terms: -1x + 1x = 0 -2k + 2kx = kx + -1 + k(-1 + 0 + x2) -2k + 2kx = kx + -1 + k(-1 + x2) -2k + 2kx = kx + -1 + (-1 * k + x2 * k) -2k + 2kx = kx + -1 + (-1k + kx2) Reorder the terms: -2k + 2kx = -1 + -1k + kx + kx2 Solving -2k + 2kx = -1 + -1k + kx + kx2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. -2k + k + 2kx = -1 + -1k + kx + k + kx2 Combine like terms: -2k + k = -1k -1k + 2kx = -1 + -1k + kx + k + kx2 Reorder the terms: -1k + 2kx = -1 + -1k + k + kx + kx2 Combine like terms: -1k + k = 0 -1k + 2kx = -1 + 0 + kx + kx2 -1k + 2kx = -1 + kx + kx2 Add '-1kx' to each side of the equation. -1k + 2kx + -1kx = -1 + kx + -1kx + kx2 Combine like terms: 2kx + -1kx = 1kx -1k + 1kx = -1 + kx + -1kx + kx2 Combine like terms: kx + -1kx = 0 -1k + 1kx = -1 + 0 + kx2 -1k + 1kx = -1 + kx2 Add '-1kx2' to each side of the equation. -1k + 1kx + -1kx2 = -1 + kx2 + -1kx2 Combine like terms: kx2 + -1kx2 = 0 -1k + 1kx + -1kx2 = -1 + 0 -1k + 1kx + -1kx2 = -1 Reorder the terms: 1 + -1k + 1kx + -1kx2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -1k + 1kx + -1kx2 = 0 The solution to this equation could not be determined.
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