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Simplifying 2(f + -4g) + -1(f + 2g) = 0 (f * 2 + -4g * 2) + -1(f + 2g) = 0 (2f + -8g) + -1(f + 2g) = 0 2f + -8g + (f * -1 + 2g * -1) = 0 2f + -8g + (-1f + -2g) = 0 Reorder the terms: 2f + -1f + -8g + -2g = 0 Combine like terms: 2f + -1f = 1f 1f + -8g + -2g = 0 Combine like terms: -8g + -2g = -10g 1f + -10g = 0 Solving 1f + -10g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '10g' to each side of the equation. 1f + -10g + 10g = 0 + 10g Combine like terms: -10g + 10g = 0 1f + 0 = 0 + 10g 1f = 0 + 10g Remove the zero: 1f = 10g Divide each side by '1'. f = 10g Simplifying f = 10g
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