3c^2+9cd-84d^2=0

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Solution for 3c^2+9cd-84d^2=0 equation:


Simplifying
3c2 + 9cd + -84d2 = 0

Reorder the terms:
9cd + 3c2 + -84d2 = 0

Solving
9cd + 3c2 + -84d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3cd + c2 + -28d2) = 0

Factor a trinomial.
3((c + -4d)(c + 7d)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(c + -4d)' equal to zero and attempt to solve:

Simplifying
c + -4d = 0

Solving
c + -4d = 0

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

Add '4d' to each side of the equation.
c + -4d + 4d = 0 + 4d

Combine like terms: -4d + 4d = 0
c + 0 = 0 + 4d
c = 0 + 4d
Remove the zero:
c = 4d

Simplifying
c = 4d

Subproblem 2
Set the factor '(c + 7d)' equal to zero and attempt to solve:

Simplifying
c + 7d = 0

Solving
c + 7d = 0

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

Add '-7d' to each side of the equation.
c + 7d + -7d = 0 + -7d

Combine like terms: 7d + -7d = 0
c + 0 = 0 + -7d
c = 0 + -7d
Remove the zero:
c = -7d

Simplifying
c = -7d
Solution
c = {4d, -7d}

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