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Simplifying (f + -1g)(x) = ((3x2 + -24x + 36) + (x + -6)) Reorder the terms for easier multiplication: x(f + -1g) = ((3x2 + -24x + 36) + (x + -6)) (f * x + -1g * x) = ((3x2 + -24x + 36) + (x + -6)) (fx + -1gx) = ((3x2 + -24x + 36) + (x + -6)) Reorder the terms: fx + -1gx = ((36 + -24x + 3x2) + (x + -6)) Remove parenthesis around (36 + -24x + 3x2) fx + -1gx = (36 + -24x + 3x2 + (x + -6)) Reorder the terms: fx + -1gx = (36 + -24x + 3x2 + (-6 + x)) Remove parenthesis around (-6 + x) fx + -1gx = (36 + -24x + 3x2 + -6 + x) Reorder the terms: fx + -1gx = (36 + -6 + -24x + x + 3x2) Combine like terms: 36 + -6 = 30 fx + -1gx = (30 + -24x + x + 3x2) Combine like terms: -24x + x = -23x fx + -1gx = (30 + -23x + 3x2) Remove parenthesis around (30 + -23x + 3x2) fx + -1gx = 30 + -23x + 3x2 Solving fx + -1gx = 30 + -23x + 3x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add 'gx' to each side of the equation. fx + -1gx + gx = 30 + -23x + gx + 3x2 Combine like terms: -1gx + gx = 0 fx + 0 = 30 + -23x + gx + 3x2 fx = 30 + -23x + gx + 3x2 Reorder the terms: fx = 30 + gx + -23x + 3x2 Divide each side by 'x'. f = 30x-1 + g + -23 + 3x Simplifying f = 30x-1 + g + -23 + 3x Reorder the terms: f = -23 + g + 30x-1 + 3x
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