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Simplifying f(n) = 2x(n + -1) + f(n + -2) Multiply f * n fn = 2x(n + -1) + f(n + -2) Reorder the terms: fn = 2x(-1 + n) + f(n + -2) fn = (-1 * 2x + n * 2x) + f(n + -2) Reorder the terms: fn = (2nx + -2x) + f(n + -2) fn = (2nx + -2x) + f(n + -2) Reorder the terms: fn = 2nx + -2x + f(-2 + n) fn = 2nx + -2x + (-2 * f + n * f) fn = 2nx + -2x + (-2f + fn) Reorder the terms: fn = -2f + fn + 2nx + -2x Add '-1fn' to each side of the equation. fn + -1fn = -2f + fn + 2nx + -1fn + -2x Combine like terms: fn + -1fn = 0 0 = -2f + fn + 2nx + -1fn + -2x Reorder the terms: 0 = -2f + fn + -1fn + 2nx + -2x Combine like terms: fn + -1fn = 0 0 = -2f + 0 + 2nx + -2x 0 = -2f + 2nx + -2x Solving 0 = -2f + 2nx + -2x Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2f' to each side of the equation. 0 + 2f = -2f + 2nx + 2f + -2x Remove the zero: 2f = -2f + 2nx + 2f + -2x Reorder the terms: 2f = -2f + 2f + 2nx + -2x Combine like terms: -2f + 2f = 0 2f = 0 + 2nx + -2x 2f = 2nx + -2x Divide each side by '2'. f = nx + -1x Simplifying f = nx + -1x
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