-7a(3x-4b+1)=-21x+ab-a

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Solution for -7a(3x-4b+1)=-21x+ab-a equation: 


Simplifying
-7a(3x + -4b + 1) = -21x + ab + -1a

Reorder the terms:
-7a(1 + -4b + 3x) = -21x + ab + -1a
(1 * -7a + -4b * -7a + 3x * -7a) = -21x + ab + -1a
(-7a + 28ab + -21ax) = -21x + ab + -1a

Reorder the terms:
-7a + 28ab + -21ax = -1a + ab + -21x

Solving
-7a + 28ab + -21ax = -1a + ab + -21x

Solving for variable 'a'.

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

Add 'a' to each side of the equation.
-7a + 28ab + a + -21ax = -1a + ab + a + -21x

Reorder the terms:
-7a + a + 28ab + -21ax = -1a + ab + a + -21x

Combine like terms: -7a + a = -6a
-6a + 28ab + -21ax = -1a + ab + a + -21x

Reorder the terms:
-6a + 28ab + -21ax = -1a + a + ab + -21x

Combine like terms: -1a + a = 0
-6a + 28ab + -21ax = 0 + ab + -21x
-6a + 28ab + -21ax = ab + -21x

Add '-1ab' to each side of the equation.
-6a + 28ab + -1ab + -21ax = ab + -1ab + -21x

Combine like terms: 28ab + -1ab = 27ab
-6a + 27ab + -21ax = ab + -1ab + -21x

Combine like terms: ab + -1ab = 0
-6a + 27ab + -21ax = 0 + -21x
-6a + 27ab + -21ax = -21x

Combine like terms: -21x + 21x = 0
-6a + 27ab + -21ax + 21x = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2a + 9ab + -7ax + 7x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2a + 9ab + -7ax + 7x)' equal to zero and attempt to solve:

Simplifying
-2a + 9ab + -7ax + 7x = 0

Solving
-2a + 9ab + -7ax + 7x = 0

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

Add '-7x' to each side of the equation.
-2a + 9ab + -7ax + 7x + -7x = 0 + -7x

Combine like terms: 7x + -7x = 0
-2a + 9ab + -7ax + 0 = 0 + -7x
-2a + 9ab + -7ax = 0 + -7x
Remove the zero:
-2a + 9ab + -7ax = -7x

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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