2a+x(3a+b)=ax+xb

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Solution for 2a+x(3a+b)=ax+xb equation: 


Simplifying
2a + x(3a + b) = ax + xb
2a + (3a * x + b * x) = ax + xb
2a + (3ax + bx) = ax + xb

Add '-1bx' to each side of the equation.
2a + 3ax + bx + -1bx = ax + bx + -1bx

Combine like terms: bx + -1bx = 0
2a + 3ax + 0 = ax + bx + -1bx
2a + 3ax = ax + bx + -1bx

Combine like terms: bx + -1bx = 0
2a + 3ax = ax + 0
2a + 3ax = ax

Solving
2a + 3ax = ax

Solving for variable 'a'.

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

Add '-1ax' to each side of the equation.
2a + 3ax + -1ax = ax + -1ax

Combine like terms: 3ax + -1ax = 2ax
2a + 2ax = ax + -1ax

Combine like terms: ax + -1ax = 0
2a + 2ax = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(1 + x) = 0

Ignore the factor 2.

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Add '-1x' to each side of the equation.
x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
0 = -1 + -1x

Simplifying
0 = -1 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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