(5c+d)(8c-d)=

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Solution for (5c+d)(8c-d)= equation: 


Simplifying
(5c + d)(8c + -1d) = 0

Multiply (5c + d) * (8c + -1d)
(5c * (8c + -1d) + d(8c + -1d)) = 0
((8c * 5c + -1d * 5c) + d(8c + -1d)) = 0

Reorder the terms:
((-5cd + 40c2) + d(8c + -1d)) = 0
((-5cd + 40c2) + d(8c + -1d)) = 0
(-5cd + 40c2 + (8c * d + -1d * d)) = 0
(-5cd + 40c2 + (8cd + -1d2)) = 0

Reorder the terms:
(-5cd + 8cd + 40c2 + -1d2) = 0

Combine like terms: -5cd + 8cd = 3cd
(3cd + 40c2 + -1d2) = 0

Solving
3cd + 40c2 + -1d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(8c + -1d)(5c + d) = 0


Subproblem 1
Set the factor '(8c + -1d)' equal to zero and attempt to solve:

Simplifying
8c + -1d = 0

Solving
8c + -1d = 0

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

Add 'd' to each side of the equation.
8c + -1d + d = 0 + d

Combine like terms: -1d + d = 0
8c + 0 = 0 + d
8c = 0 + d
Remove the zero:
8c = d

Divide each side by '8'.
c = 0.125d

Simplifying
c = 0.125d

Subproblem 2
Set the factor '(5c + d)' equal to zero and attempt to solve:

Simplifying
5c + d = 0

Solving
5c + d = 0

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

Add '-1d' to each side of the equation.
5c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
5c + 0 = 0 + -1d
5c = 0 + -1d
Remove the zero:
5c = -1d

Divide each side by '5'.
c = -0.2d

Simplifying
c = -0.2d
Solution
c = {0.125d, -0.2d}

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