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Simplifying
(7c + 4d)(7c + -4d) = 0
Multiply (7c + 4d) * (7c + -4d)
(7c * (7c + -4d) + 4d * (7c + -4d)) = 0
((7c * 7c + -4d * 7c) + 4d * (7c + -4d)) = 0
Reorder the terms:
((-28cd + 49c2) + 4d * (7c + -4d)) = 0
((-28cd + 49c2) + 4d * (7c + -4d)) = 0
(-28cd + 49c2 + (7c * 4d + -4d * 4d)) = 0
(-28cd + 49c2 + (28cd + -16d2)) = 0
Reorder the terms:
(-28cd + 28cd + 49c2 + -16d2) = 0
Combine like terms: -28cd + 28cd = 0
(0 + 49c2 + -16d2) = 0
(49c2 + -16d2) = 0
Solving
49c2 + -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.
49c2 + -16d2 + 16d2 = 0 + 16d2
Combine like terms: -16d2 + 16d2 = 0
49c2 + 0 = 0 + 16d2
49c2 = 0 + 16d2
Remove the zero:
49c2 = 16d2
Divide each side by '49'.
c2 = 0.3265306122d2
Simplifying
c2 = 0.3265306122d2
Take the square root of each side:
c = {-0.571428571d, 0.571428571d}
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