(2c+6d)(c-d)=

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Solution for (2c+6d)(c-d)= equation: 


Simplifying
(2c + 6d)(c + -1d) = 0

Multiply (2c + 6d) * (c + -1d)
(2c * (c + -1d) + 6d * (c + -1d)) = 0
((c * 2c + -1d * 2c) + 6d * (c + -1d)) = 0

Reorder the terms:
((-2cd + 2c2) + 6d * (c + -1d)) = 0
((-2cd + 2c2) + 6d * (c + -1d)) = 0
(-2cd + 2c2 + (c * 6d + -1d * 6d)) = 0
(-2cd + 2c2 + (6cd + -6d2)) = 0

Reorder the terms:
(-2cd + 6cd + 2c2 + -6d2) = 0

Combine like terms: -2cd + 6cd = 4cd
(4cd + 2c2 + -6d2) = 0

Solving
4cd + 2c2 + -6d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2cd + c2 + -3d2) = 0

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

Ignore the factor 2.

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

Simplifying
c + -1d = 0

Solving
c + -1d = 0

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

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

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

Simplifying
c = d

Subproblem 2
Set the factor '(c + 3d)' equal to zero and attempt to solve:

Simplifying
c + 3d = 0

Solving
c + 3d = 0

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

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

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

Simplifying
c = -3d
Solution
c = {d, -3d}

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