5(2c+d)6(c+2d)=

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Solution for 5(2c+d)6(c+2d)= equation: 


Simplifying
5(2c + d) * 6(c + 2d) = 0

Reorder the terms for easier multiplication:
5 * 6(2c + d)(c + 2d) = 0

Multiply 5 * 6
30(2c + d)(c + 2d) = 0

Multiply (2c + d) * (c + 2d)
30(2c * (c + 2d) + d(c + 2d)) = 0
30((c * 2c + 2d * 2c) + d(c + 2d)) = 0

Reorder the terms:
30((4cd + 2c2) + d(c + 2d)) = 0
30((4cd + 2c2) + d(c + 2d)) = 0
30(4cd + 2c2 + (c * d + 2d * d)) = 0
30(4cd + 2c2 + (cd + 2d2)) = 0

Reorder the terms:
30(4cd + cd + 2c2 + 2d2) = 0

Combine like terms: 4cd + cd = 5cd
30(5cd + 2c2 + 2d2) = 0
(5cd * 30 + 2c2 * 30 + 2d2 * 30) = 0
(150cd + 60c2 + 60d2) = 0

Solving
150cd + 60c2 + 60d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '30'.
30(5cd + 2c2 + 2d2) = 0

Factor a trinomial.
30((2c + d)(c + 2d)) = 0

Ignore the factor 30.

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

Simplifying
2c + d = 0

Solving
2c + d = 0

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

Add '-1d' to each side of the equation.
2c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
2c + 0 = 0 + -1d
2c = 0 + -1d
Remove the zero:
2c = -1d

Divide each side by '2'.
c = -0.5d

Simplifying
c = -0.5d

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 = {-0.5d, -2d}

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