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Simplifying
(5c + 4d)(5c + -4d) = 0
Multiply (5c + 4d) * (5c + -4d)
(5c * (5c + -4d) + 4d * (5c + -4d)) = 0
((5c * 5c + -4d * 5c) + 4d * (5c + -4d)) = 0
Reorder the terms:
((-20cd + 25c2) + 4d * (5c + -4d)) = 0
((-20cd + 25c2) + 4d * (5c + -4d)) = 0
(-20cd + 25c2 + (5c * 4d + -4d * 4d)) = 0
(-20cd + 25c2 + (20cd + -16d2)) = 0
Reorder the terms:
(-20cd + 20cd + 25c2 + -16d2) = 0
Combine like terms: -20cd + 20cd = 0
(0 + 25c2 + -16d2) = 0
(25c2 + -16d2) = 0
Solving
25c2 + -16d2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '16d2' to each side of the equation.
25c2 + -16d2 + 16d2 = 0 + 16d2
Combine like terms: -16d2 + 16d2 = 0
25c2 + 0 = 0 + 16d2
25c2 = 0 + 16d2
Remove the zero:
25c2 = 16d2
Divide each side by '25'.
c2 = 0.64d2
Simplifying
c2 = 0.64d2
Take the square root of each side:
c = {-0.8d, 0.8d}
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