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Simplifying
(4c + -3d)(4c + 3d) = 0
Multiply (4c + -3d) * (4c + 3d)
(4c * (4c + 3d) + -3d * (4c + 3d)) = 0
((4c * 4c + 3d * 4c) + -3d * (4c + 3d)) = 0
Reorder the terms:
((12cd + 16c2) + -3d * (4c + 3d)) = 0
((12cd + 16c2) + -3d * (4c + 3d)) = 0
(12cd + 16c2 + (4c * -3d + 3d * -3d)) = 0
(12cd + 16c2 + (-12cd + -9d2)) = 0
Reorder the terms:
(12cd + -12cd + 16c2 + -9d2) = 0
Combine like terms: 12cd + -12cd = 0
(0 + 16c2 + -9d2) = 0
(16c2 + -9d2) = 0
Solving
16c2 + -9d2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '9d2' to each side of the equation.
16c2 + -9d2 + 9d2 = 0 + 9d2
Combine like terms: -9d2 + 9d2 = 0
16c2 + 0 = 0 + 9d2
16c2 = 0 + 9d2
Remove the zero:
16c2 = 9d2
Divide each side by '16'.
c2 = 0.5625d2
Simplifying
c2 = 0.5625d2
Take the square root of each side:
c = {-0.75d, 0.75d}
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