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Simplifying x(k + 2) + -3x(k + 1) + 2x(k) = 0 Reorder the terms: x(2 + k) + -3x(k + 1) + 2x(k) = 0 (2 * x + k * x) + -3x(k + 1) + 2x(k) = 0 Reorder the terms: (kx + 2x) + -3x(k + 1) + 2x(k) = 0 (kx + 2x) + -3x(k + 1) + 2x(k) = 0 Reorder the terms: kx + 2x + -3x(1 + k) + 2x(k) = 0 kx + 2x + (1 * -3x + k * -3x) + 2x(k) = 0 Reorder the terms: kx + 2x + (-3kx + -3x) + 2x(k) = 0 kx + 2x + (-3kx + -3x) + 2x(k) = 0 Multiply x * k kx + 2x + -3kx + -3x + 2kx = 0 Reorder the terms: kx + -3kx + 2kx + 2x + -3x = 0 Combine like terms: kx + -3kx = -2kx -2kx + 2kx + 2x + -3x = 0 Combine like terms: -2kx + 2kx = 0 0 + 2x + -3x = 0 2x + -3x = 0 Combine like terms: 2x + -3x = -1x -1x = 0 Solving -1x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '-1'. x = 0 Simplifying x = 0
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