3(a+b)+6n(a+b)=

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Solution for 3(a+b)+6n(a+b)= equation: 


Simplifying
3(a + b) + 6n(a + b) = 0
(a * 3 + b * 3) + 6n(a + b) = 0
(3a + 3b) + 6n(a + b) = 0
3a + 3b + (a * 6n + b * 6n) = 0
3a + 3b + (6an + 6bn) = 0

Reorder the terms:
3a + 6an + 3b + 6bn = 0

Solving
3a + 6an + 3b + 6bn = 0

Solving for variable 'a'.

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

Add '-3b' to each side of the equation.
3a + 6an + 3b + -3b + 6bn = 0 + -3b

Combine like terms: 3b + -3b = 0
3a + 6an + 0 + 6bn = 0 + -3b
3a + 6an + 6bn = 0 + -3b
Remove the zero:
3a + 6an + 6bn = -3b

Add '-6bn' to each side of the equation.
3a + 6an + 6bn + -6bn = -3b + -6bn

Combine like terms: 6bn + -6bn = 0
3a + 6an + 0 = -3b + -6bn
3a + 6an = -3b + -6bn

Reorder the terms:
3a + 6an + 3b + 6bn = -3b + 3b + -6bn + 6bn

Combine like terms: -3b + 3b = 0
3a + 6an + 3b + 6bn = 0 + -6bn + 6bn
3a + 6an + 3b + 6bn = -6bn + 6bn

Combine like terms: -6bn + 6bn = 0
3a + 6an + 3b + 6bn = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(a + 2an + b + 2bn) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(a + 2an + b + 2bn)' equal to zero and attempt to solve:

Simplifying
a + 2an + b + 2bn = 0

Solving
a + 2an + b + 2bn = 0

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

Add '-1b' to each side of the equation.
a + 2an + b + -1b + 2bn = 0 + -1b

Combine like terms: b + -1b = 0
a + 2an + 0 + 2bn = 0 + -1b
a + 2an + 2bn = 0 + -1b
Remove the zero:
a + 2an + 2bn = -1b

Add '-2bn' to each side of the equation.
a + 2an + 2bn + -2bn = -1b + -2bn

Combine like terms: 2bn + -2bn = 0
a + 2an + 0 = -1b + -2bn
a + 2an = -1b + -2bn

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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