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Simplifying 6(2g + -4h) + -1(3G + -7h) = 0 (2g * 6 + -4h * 6) + -1(3G + -7h) = 0 (12g + -24h) + -1(3G + -7h) = 0 12g + -24h + (3G * -1 + -7h * -1) = 0 12g + -24h + (-3G + 7h) = 0 Reorder the terms: -3G + 12g + -24h + 7h = 0 Combine like terms: -24h + 7h = -17h -3G + 12g + -17h = 0 Solving -3G + 12g + -17h = 0 Solving for variable 'G'. Move all terms containing G to the left, all other terms to the right. Add '-12g' to each side of the equation. -3G + 12g + -12g + -17h = 0 + -12g Combine like terms: 12g + -12g = 0 -3G + 0 + -17h = 0 + -12g -3G + -17h = 0 + -12g Remove the zero: -3G + -17h = -12g Add '17h' to each side of the equation. -3G + -17h + 17h = -12g + 17h Combine like terms: -17h + 17h = 0 -3G + 0 = -12g + 17h -3G = -12g + 17h Divide each side by '-3'. G = 4g + -5.666666667h Simplifying G = 4g + -5.666666667h
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