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Simplifying
(5r + 4d)(5r + -4d) = 0
Reorder the terms:
(4d + 5r)(5r + -4d) = 0
Reorder the terms:
(4d + 5r)(-4d + 5r) = 0
Multiply (4d + 5r) * (-4d + 5r)
(4d * (-4d + 5r) + 5r * (-4d + 5r)) = 0
((-4d * 4d + 5r * 4d) + 5r * (-4d + 5r)) = 0
Reorder the terms:
((20dr + -16d2) + 5r * (-4d + 5r)) = 0
((20dr + -16d2) + 5r * (-4d + 5r)) = 0
(20dr + -16d2 + (-4d * 5r + 5r * 5r)) = 0
(20dr + -16d2 + (-20dr + 25r2)) = 0
Reorder the terms:
(20dr + -20dr + -16d2 + 25r2) = 0
Combine like terms: 20dr + -20dr = 0
(0 + -16d2 + 25r2) = 0
(-16d2 + 25r2) = 0
Solving
-16d2 + 25r2 = 0
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-25r2' to each side of the equation.
-16d2 + 25r2 + -25r2 = 0 + -25r2
Combine like terms: 25r2 + -25r2 = 0
-16d2 + 0 = 0 + -25r2
-16d2 = 0 + -25r2
Remove the zero:
-16d2 = -25r2
Divide each side by '-16'.
d2 = 1.5625r2
Simplifying
d2 = 1.5625r2
Take the square root of each side:
d = {-1.25r, 1.25r}
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