abs(3xa+10)=abs(4xa-2)

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Solution for abs(3xa+10)=abs(4xa-2) equation: 


Simplifying
abs(3xa + 10) = abs(4xa + -2)

Reorder the terms:
abs(10 + 3ax) = abs(4xa + -2)
(10 * abs + 3ax * abs) = abs(4xa + -2)
(10abs + 3a2bsx) = abs(4xa + -2)

Reorder the terms:
10abs + 3a2bsx = abs(-2 + 4ax)
10abs + 3a2bsx = (-2 * abs + 4ax * abs)
10abs + 3a2bsx = (-2abs + 4a2bsx)

Solving
10abs + 3a2bsx = -2abs + 4a2bsx

Solving for variable 'a'.

Reorder the terms:
10abs + 2abs + 3a2bsx + -4a2bsx = -2abs + 4a2bsx + 2abs + -4a2bsx

Combine like terms: 10abs + 2abs = 12abs
12abs + 3a2bsx + -4a2bsx = -2abs + 4a2bsx + 2abs + -4a2bsx

Combine like terms: 3a2bsx + -4a2bsx = -1a2bsx
12abs + -1a2bsx = -2abs + 4a2bsx + 2abs + -4a2bsx

Reorder the terms:
12abs + -1a2bsx = -2abs + 2abs + 4a2bsx + -4a2bsx

Combine like terms: -2abs + 2abs = 0
12abs + -1a2bsx = 0 + 4a2bsx + -4a2bsx
12abs + -1a2bsx = 4a2bsx + -4a2bsx

Combine like terms: 4a2bsx + -4a2bsx = 0
12abs + -1a2bsx = 0

Factor out the Greatest Common Factor (GCF), 'abs'.
abs(12 + -1ax) = 0


Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve:

Simplifying
abs = 0

Solving
abs = 0

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

Simplifying
abs = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(12 + -1ax)' equal to zero and attempt to solve:

Simplifying
12 + -1ax = 0

Solving
12 + -1ax = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1ax = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1ax = 0 + -12
-1ax = 0 + -12

Combine like terms: 0 + -12 = -12
-1ax = -12

Divide each side by '-1x'.
a = 12x-1

Simplifying
a = 12x-1
Solution
a = {12x-1}

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