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Simplifying 1 + (d3 + ad2 + bd + c) = ed Reorder the terms: 1 + (ad2 + bd + c + d3) = ed Remove parenthesis around (ad2 + bd + c + d3) 1 + ad2 + bd + c + d3 = ed Solving 1 + ad2 + bd + c + d3 = de Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + ad2 + bd + c + -1 + d3 = -1 + de Reorder the terms: 1 + -1 + ad2 + bd + c + d3 = -1 + de Combine like terms: 1 + -1 = 0 0 + ad2 + bd + c + d3 = -1 + de ad2 + bd + c + d3 = -1 + de Add '-1bd' to each side of the equation. ad2 + bd + c + -1bd + d3 = -1 + -1bd + de Reorder the terms: ad2 + bd + -1bd + c + d3 = -1 + -1bd + de Combine like terms: bd + -1bd = 0 ad2 + 0 + c + d3 = -1 + -1bd + de ad2 + c + d3 = -1 + -1bd + de Add '-1c' to each side of the equation. ad2 + c + -1c + d3 = -1 + -1bd + -1c + de Combine like terms: c + -1c = 0 ad2 + 0 + d3 = -1 + -1bd + -1c + de ad2 + d3 = -1 + -1bd + -1c + de Add '-1d3' to each side of the equation. ad2 + d3 + -1d3 = -1 + -1bd + -1c + de + -1d3 Combine like terms: d3 + -1d3 = 0 ad2 + 0 = -1 + -1bd + -1c + de + -1d3 ad2 = -1 + -1bd + -1c + de + -1d3 Divide each side by 'd2'. a = -1d-2 + -1bd-1 + -1cd-2 + d-1e + -1d Simplifying a = -1d-2 + -1bd-1 + -1cd-2 + d-1e + -1d Reorder the terms: a = -1bd-1 + -1cd-2 + -1d-2 + d-1e + -1d
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