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Simplifying 3(3f + 2g) + -3(4f + 3g) = 0 (3f * 3 + 2g * 3) + -3(4f + 3g) = 0 (9f + 6g) + -3(4f + 3g) = 0 9f + 6g + (4f * -3 + 3g * -3) = 0 9f + 6g + (-12f + -9g) = 0 Reorder the terms: 9f + -12f + 6g + -9g = 0 Combine like terms: 9f + -12f = -3f -3f + 6g + -9g = 0 Combine like terms: 6g + -9g = -3g -3f + -3g = 0 Solving -3f + -3g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '3g' to each side of the equation. -3f + -3g + 3g = 0 + 3g Combine like terms: -3g + 3g = 0 -3f + 0 = 0 + 3g -3f = 0 + 3g Remove the zero: -3f = 3g Divide each side by '-3'. f = -1g Simplifying f = -1g
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