(3c-1d)(5c-7d)=

Solution for (3c-1d)(5c-7d)= equation:

Simplifying
(3c + -1d)(5c + -7d) = 0

Multiply (3c + -1d) * (5c + -7d)
(3c * (5c + -7d) + -1d * (5c + -7d)) = 0
((5c * 3c + -7d * 3c) + -1d * (5c + -7d)) = 0

Reorder the terms:
((-21cd + 15c2) + -1d * (5c + -7d)) = 0
((-21cd + 15c2) + -1d * (5c + -7d)) = 0
(-21cd + 15c2 + (5c * -1d + -7d * -1d)) = 0
(-21cd + 15c2 + (-5cd + 7d2)) = 0

Reorder the terms:
(-21cd + -5cd + 15c2 + 7d2) = 0

Combine like terms: -21cd + -5cd = -26cd
(-26cd + 15c2 + 7d2) = 0

Solving
-26cd + 15c2 + 7d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5c + -7d)(3c + -1d) = 0

Subproblem 1
Set the factor '(5c + -7d)' equal to zero and attempt to solve:

Simplifying
5c + -7d = 0

Solving
5c + -7d = 0

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

Add '7d' to each side of the equation.
5c + -7d + 7d = 0 + 7d

Combine like terms: -7d + 7d = 0
5c + 0 = 0 + 7d
5c = 0 + 7d
Remove the zero:
5c = 7d

Divide each side by '5'.
c = 1.4d

Simplifying
c = 1.4d
Subproblem 2
Set the factor '(3c + -1d)' equal to zero and attempt to solve:

Simplifying
3c + -1d = 0

Solving
3c + -1d = 0

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

Add 'd' to each side of the equation.
3c + -1d + d = 0 + d

Combine like terms: -1d + d = 0
3c + 0 = 0 + d
3c = 0 + d
Remove the zero:
3c = d

Divide each side by '3'.
c = 0.3333333333d

Simplifying
c = 0.3333333333d
Solution
c = {1.4d, 0.3333333333d}