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Simplifying (5f + -1g) + -1(3f + g) = 0 Remove parenthesis around (5f + -1g) 5f + -1g + -1(3f + g) = 0 5f + -1g + (3f * -1 + g * -1) = 0 5f + -1g + (-3f + -1g) = 0 Reorder the terms: 5f + -3f + -1g + -1g = 0 Combine like terms: 5f + -3f = 2f 2f + -1g + -1g = 0 Combine like terms: -1g + -1g = -2g 2f + -2g = 0 Solving 2f + -2g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2g' to each side of the equation. 2f + -2g + 2g = 0 + 2g Combine like terms: -2g + 2g = 0 2f + 0 = 0 + 2g 2f = 0 + 2g Remove the zero: 2f = 2g Divide each side by '2'. f = g Simplifying f = g
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