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Simplifying (7r + 5g)(7r + -5g) = 0 Reorder the terms: (5g + 7r)(7r + -5g) = 0 Reorder the terms: (5g + 7r)(-5g + 7r) = 0 Multiply (5g + 7r) * (-5g + 7r) (5g * (-5g + 7r) + 7r * (-5g + 7r)) = 0 ((-5g * 5g + 7r * 5g) + 7r * (-5g + 7r)) = 0 Reorder the terms: ((35gr + -25g2) + 7r * (-5g + 7r)) = 0 ((35gr + -25g2) + 7r * (-5g + 7r)) = 0 (35gr + -25g2 + (-5g * 7r + 7r * 7r)) = 0 (35gr + -25g2 + (-35gr + 49r2)) = 0 Reorder the terms: (35gr + -35gr + -25g2 + 49r2) = 0 Combine like terms: 35gr + -35gr = 0 (0 + -25g2 + 49r2) = 0 (-25g2 + 49r2) = 0 Solving -25g2 + 49r2 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-49r2' to each side of the equation. -25g2 + 49r2 + -49r2 = 0 + -49r2 Combine like terms: 49r2 + -49r2 = 0 -25g2 + 0 = 0 + -49r2 -25g2 = 0 + -49r2 Remove the zero: -25g2 = -49r2 Divide each side by '-25'. g2 = 1.96r2 Simplifying g2 = 1.96r2 Take the square root of each side: g = {-1.4r, 1.4r}
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