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Simplifying 2(f + g)(g + j) = 5g Multiply (f + g) * (g + j) 2(f(g + j) + g(g + j)) = 5g 2((g * f + j * f) + g(g + j)) = 5g 2((fg + fj) + g(g + j)) = 5g 2(fg + fj + (g * g + j * g)) = 5g Reorder the terms: 2(fg + fj + (gj + g2)) = 5g 2(fg + fj + (gj + g2)) = 5g 2(fg + fj + gj + g2) = 5g (fg * 2 + fj * 2 + gj * 2 + g2 * 2) = 5g (2fg + 2fj + 2gj + 2g2) = 5g Solving 2fg + 2fj + 2gj + 2g2 = 5g Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-2gj' to each side of the equation. 2fg + 2fj + 2gj + -2gj + 2g2 = 5g + -2gj Combine like terms: 2gj + -2gj = 0 2fg + 2fj + 0 + 2g2 = 5g + -2gj 2fg + 2fj + 2g2 = 5g + -2gj Add '-2g2' to each side of the equation. 2fg + 2fj + 2g2 + -2g2 = 5g + -2gj + -2g2 Combine like terms: 2g2 + -2g2 = 0 2fg + 2fj + 0 = 5g + -2gj + -2g2 2fg + 2fj = 5g + -2gj + -2g2 Reorder the terms: 2fg + 2fj + -5g + 2gj + 2g2 = 5g + -5g + -2gj + 2gj + -2g2 + 2g2 Combine like terms: 5g + -5g = 0 2fg + 2fj + -5g + 2gj + 2g2 = 0 + -2gj + 2gj + -2g2 + 2g2 2fg + 2fj + -5g + 2gj + 2g2 = -2gj + 2gj + -2g2 + 2g2 Combine like terms: -2gj + 2gj = 0 2fg + 2fj + -5g + 2gj + 2g2 = 0 + -2g2 + 2g2 2fg + 2fj + -5g + 2gj + 2g2 = -2g2 + 2g2 Combine like terms: -2g2 + 2g2 = 0 2fg + 2fj + -5g + 2gj + 2g2 = 0 The solution to this equation could not be determined.
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