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Simplifying (a + c + -1e) * f = (b + 1000 + -1c + -1f) * e Reorder the terms for easier multiplication: f(a + c + -1e) = (b + 1000 + -1c + -1f) * e (a * f + c * f + -1e * f) = (b + 1000 + -1c + -1f) * e (af + cf + -1ef) = (b + 1000 + -1c + -1f) * e Reorder the terms: af + cf + -1ef = (1000 + b + -1c + -1f) * e Reorder the terms for easier multiplication: af + cf + -1ef = e(1000 + b + -1c + -1f) af + cf + -1ef = (1000 * e + b * e + -1c * e + -1f * e) Reorder the terms: af + cf + -1ef = (be + -1ce + 1000e + -1ef) af + cf + -1ef = (be + -1ce + 1000e + -1ef) Add 'ef' to each side of the equation. af + cf + -1ef + ef = be + -1ce + 1000e + -1ef + ef Combine like terms: -1ef + ef = 0 af + cf + 0 = be + -1ce + 1000e + -1ef + ef af + cf = be + -1ce + 1000e + -1ef + ef Combine like terms: -1ef + ef = 0 af + cf = be + -1ce + 1000e + 0 af + cf = be + -1ce + 1000e Solving af + cf = be + -1ce + 1000e Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1cf' to each side of the equation. af + cf + -1cf = be + -1ce + -1cf + 1000e Combine like terms: cf + -1cf = 0 af + 0 = be + -1ce + -1cf + 1000e af = be + -1ce + -1cf + 1000e Divide each side by 'f'. a = bef-1 + -1cef-1 + -1c + 1000ef-1 Simplifying a = bef-1 + -1cef-1 + -1c + 1000ef-1 Reorder the terms: a = bef-1 + -1c + -1cef-1 + 1000ef-1
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