(5c-3d)(2c+4d)=

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Solution for (5c-3d)(2c+4d)= equation: 


Simplifying
(5c + -3d)(2c + 4d) = 0

Multiply (5c + -3d) * (2c + 4d)
(5c * (2c + 4d) + -3d * (2c + 4d)) = 0
((2c * 5c + 4d * 5c) + -3d * (2c + 4d)) = 0

Reorder the terms:
((20cd + 10c2) + -3d * (2c + 4d)) = 0
((20cd + 10c2) + -3d * (2c + 4d)) = 0
(20cd + 10c2 + (2c * -3d + 4d * -3d)) = 0
(20cd + 10c2 + (-6cd + -12d2)) = 0

Reorder the terms:
(20cd + -6cd + 10c2 + -12d2) = 0

Combine like terms: 20cd + -6cd = 14cd
(14cd + 10c2 + -12d2) = 0

Solving
14cd + 10c2 + -12d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7cd + 5c2 + -6d2) = 0

Factor a trinomial.
2((5c + -3d)(c + 2d)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5c + -3d)' equal to zero and attempt to solve:

Simplifying
5c + -3d = 0

Solving
5c + -3d = 0

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

Add '3d' to each side of the equation.
5c + -3d + 3d = 0 + 3d

Combine like terms: -3d + 3d = 0
5c + 0 = 0 + 3d
5c = 0 + 3d
Remove the zero:
5c = 3d

Divide each side by '5'.
c = 0.6d

Simplifying
c = 0.6d

Subproblem 2
Set the factor '(c + 2d)' equal to zero and attempt to solve:

Simplifying
c + 2d = 0

Solving
c + 2d = 0

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

Add '-2d' to each side of the equation.
c + 2d + -2d = 0 + -2d

Combine like terms: 2d + -2d = 0
c + 0 = 0 + -2d
c = 0 + -2d
Remove the zero:
c = -2d

Simplifying
c = -2d
Solution
c = {0.6d, -2d}

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