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Simplifying
(3r + 5d)(3r + -5d) = 0
Reorder the terms:
(5d + 3r)(3r + -5d) = 0
Reorder the terms:
(5d + 3r)(-5d + 3r) = 0
Multiply (5d + 3r) * (-5d + 3r)
(5d * (-5d + 3r) + 3r * (-5d + 3r)) = 0
((-5d * 5d + 3r * 5d) + 3r * (-5d + 3r)) = 0
Reorder the terms:
((15dr + -25d2) + 3r * (-5d + 3r)) = 0
((15dr + -25d2) + 3r * (-5d + 3r)) = 0
(15dr + -25d2 + (-5d * 3r + 3r * 3r)) = 0
(15dr + -25d2 + (-15dr + 9r2)) = 0
Reorder the terms:
(15dr + -15dr + -25d2 + 9r2) = 0
Combine like terms: 15dr + -15dr = 0
(0 + -25d2 + 9r2) = 0
(-25d2 + 9r2) = 0
Solving
-25d2 + 9r2 = 0
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-9r2' to each side of the equation.
-25d2 + 9r2 + -9r2 = 0 + -9r2
Combine like terms: 9r2 + -9r2 = 0
-25d2 + 0 = 0 + -9r2
-25d2 = 0 + -9r2
Remove the zero:
-25d2 = -9r2
Divide each side by '-25'.
d2 = 0.36r2
Simplifying
d2 = 0.36r2
Take the square root of each side:
d = {-0.6r, 0.6r}
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