(3c+-1d)(3c+d)=

Solution for (3c+-1d)(3c+d)= equation:

Simplifying
(3c + -1d)(3c + d) = 0

Multiply (3c + -1d) * (3c + d)
(3c * (3c + d) + -1d * (3c + d)) = 0
((3c * 3c + d * 3c) + -1d * (3c + d)) = 0

Reorder the terms:
((3cd + 9c2) + -1d * (3c + d)) = 0
((3cd + 9c2) + -1d * (3c + d)) = 0
(3cd + 9c2 + (3c * -1d + d * -1d)) = 0
(3cd + 9c2 + (-3cd + -1d2)) = 0

Reorder the terms:
(3cd + -3cd + 9c2 + -1d2) = 0

Combine like terms: 3cd + -3cd = 0
(0 + 9c2 + -1d2) = 0
(9c2 + -1d2) = 0

Solving
9c2 + -1d2 = 0

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add 'd2' to each side of the equation.
9c2 + -1d2 + d2 = 0 + d2

Combine like terms: -1d2 + d2 = 0
9c2 + 0 = 0 + d2
9c2 = 0 + d2
Remove the zero:
9c2 = d2

Divide each side by '9'.
c2 = 0.1111111111d2

Simplifying
c2 = 0.1111111111d2

Take the square root of each side:
c = {-0.333333333d, 0.333333333d}