2(x-5)=ax-2(x+5)

Solution for 2(x-5)=ax-2(x+5) equation:

Simplifying
2(x + -5) = ax + -2(x + 5)

Reorder the terms:
2(-5 + x) = ax + -2(x + 5)
(-5 * 2 + x * 2) = ax + -2(x + 5)
(-10 + 2x) = ax + -2(x + 5)

Reorder the terms:
-10 + 2x = ax + -2(5 + x)
-10 + 2x = ax + (5 * -2 + x * -2)
-10 + 2x = ax + (-10 + -2x)

Reorder the terms:
-10 + 2x = -10 + ax + -2x

Add '10' to each side of the equation.
-10 + 10 + 2x = -10 + ax + 10 + -2x

Combine like terms: -10 + 10 = 0
0 + 2x = -10 + ax + 10 + -2x
2x = -10 + ax + 10 + -2x

Reorder the terms:
2x = -10 + 10 + ax + -2x

Combine like terms: -10 + 10 = 0
2x = 0 + ax + -2x
2x = ax + -2x

Solving
2x = ax + -2x

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2x + 2x = 4x
-1ax + 4x = -2x + 2x

Combine like terms: -2x + 2x = 0
-1ax + 4x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1a + 4) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1a + 4)' equal to zero and attempt to solve:

Simplifying
-1a + 4 = 0

Reorder the terms:
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Add 'a' to each side of the equation.
-1a + a = -4 + a

Combine like terms: -1a + a = 0
0 = -4 + a

Simplifying
0 = -4 + a

The solution to this equation could not be determined.

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