14(ac-2b)=7(b+3a)

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Solution for 14(ac-2b)=7(b+3a) equation: 


Simplifying
14(ac + -2b) = 7(b + 3a)
(ac * 14 + -2b * 14) = 7(b + 3a)
(14ac + -28b) = 7(b + 3a)

Reorder the terms:
14ac + -28b = 7(3a + b)
14ac + -28b = (3a * 7 + b * 7)
14ac + -28b = (21a + 7b)

Solving
14ac + -28b = 21a + 7b

Solving for variable 'a'.

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

Add '-21a' to each side of the equation.
14ac + -21a + -28b = 21a + -21a + 7b

Reorder the terms:
-21a + 14ac + -28b = 21a + -21a + 7b

Combine like terms: 21a + -21a = 0
-21a + 14ac + -28b = 0 + 7b
-21a + 14ac + -28b = 7b

Add '28b' to each side of the equation.
-21a + 14ac + -28b + 28b = 7b + 28b

Combine like terms: -28b + 28b = 0
-21a + 14ac + 0 = 7b + 28b
-21a + 14ac = 7b + 28b

Combine like terms: 7b + 28b = 35b
-21a + 14ac = 35b

Combine like terms: 35b + -35b = 0
-21a + 14ac + -35b = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3a + 2ac + -5b) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-3a + 2ac + -5b)' equal to zero and attempt to solve:

Simplifying
-3a + 2ac + -5b = 0

Solving
-3a + 2ac + -5b = 0

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

Add '5b' to each side of the equation.
-3a + 2ac + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
-3a + 2ac + 0 = 0 + 5b
-3a + 2ac = 0 + 5b
Remove the zero:
-3a + 2ac = 5b

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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