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

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


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

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

Reorder the terms:
0 = ((6cd + 9c2) + -3d * (3c + 2d))
0 = ((6cd + 9c2) + -3d * (3c + 2d))
0 = (6cd + 9c2 + (3c * -3d + 2d * -3d))
0 = (6cd + 9c2 + (-9cd + -6d2))

Reorder the terms:
0 = (6cd + -9cd + 9c2 + -6d2)

Combine like terms: 6cd + -9cd = -3cd
0 = (-3cd + 9c2 + -6d2)

Solving
0 = -3cd + 9c2 + -6d2

Solving for variable 'c'.
Remove the zero:
3cd + -9c2 + 6d2 = -3cd + 9c2 + -6d2 + 3cd + -9c2 + 6d2

Reorder the terms:
3cd + -9c2 + 6d2 = -3cd + 3cd + 9c2 + -9c2 + -6d2 + 6d2

Combine like terms: -3cd + 3cd = 0
3cd + -9c2 + 6d2 = 0 + 9c2 + -9c2 + -6d2 + 6d2
3cd + -9c2 + 6d2 = 9c2 + -9c2 + -6d2 + 6d2

Combine like terms: 9c2 + -9c2 = 0
3cd + -9c2 + 6d2 = 0 + -6d2 + 6d2
3cd + -9c2 + 6d2 = -6d2 + 6d2

Combine like terms: -6d2 + 6d2 = 0
3cd + -9c2 + 6d2 = 0

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

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

Ignore the factor 3.

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

Simplifying
-3c + -2d = 0

Solving
-3c + -2d = 0

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

Add '2d' to each side of the equation.
-3c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
-3c + 0 = 0 + 2d
-3c = 0 + 2d
Remove the zero:
-3c = 2d

Divide each side by '-3'.
c = -0.6666666667d

Simplifying
c = -0.6666666667d

Subproblem 2
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
Solution
c = {-0.6666666667d, d}

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