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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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