2a+6b=4at-8c

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Solution for 2a+6b=4at-8c equation: 


Simplifying
2a + 6b = 4at + -8c

Solving
2a + 6b = 4at + -8c

Solving for variable 'a'.

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

Add '-4at' to each side of the equation.
2a + -4at + 6b = 4at + -4at + -8c

Combine like terms: 4at + -4at = 0
2a + -4at + 6b = 0 + -8c
2a + -4at + 6b = -8c

Add '-6b' to each side of the equation.
2a + -4at + 6b + -6b = -6b + -8c

Combine like terms: 6b + -6b = 0
2a + -4at + 0 = -6b + -8c
2a + -4at = -6b + -8c

Reorder the terms:
2a + -4at + 6b + 8c = -6b + 6b + -8c + 8c

Combine like terms: -6b + 6b = 0
2a + -4at + 6b + 8c = 0 + -8c + 8c
2a + -4at + 6b + 8c = -8c + 8c

Combine like terms: -8c + 8c = 0
2a + -4at + 6b + 8c = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(a + -2at + 3b + 4c) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(a + -2at + 3b + 4c)' equal to zero and attempt to solve:

Simplifying
a + -2at + 3b + 4c = 0

Solving
a + -2at + 3b + 4c = 0

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

Add '-3b' to each side of the equation.
a + -2at + 3b + -3b + 4c = 0 + -3b

Combine like terms: 3b + -3b = 0
a + -2at + 0 + 4c = 0 + -3b
a + -2at + 4c = 0 + -3b
Remove the zero:
a + -2at + 4c = -3b

Add '-4c' to each side of the equation.
a + -2at + 4c + -4c = -3b + -4c

Combine like terms: 4c + -4c = 0
a + -2at + 0 = -3b + -4c
a + -2at = -3b + -4c

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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