a(2x-5)=3(ax+2a)

Solution for a(2x-5)=3(ax+2a) equation:

Simplifying
a(2x + -5) = 3(ax + 2a)

Reorder the terms:
a(-5 + 2x) = 3(ax + 2a)
(-5 * a + 2x * a) = 3(ax + 2a)
(-5a + 2ax) = 3(ax + 2a)

Reorder the terms:
-5a + 2ax = 3(2a + ax)
-5a + 2ax = (2a * 3 + ax * 3)
-5a + 2ax = (6a + 3ax)

Solving
-5a + 2ax = 6a + 3ax

Solving for variable 'a'.

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

Add '-6a' to each side of the equation.
-5a + -6a + 2ax = 6a + -6a + 3ax

Combine like terms: -5a + -6a = -11a
-11a + 2ax = 6a + -6a + 3ax

Combine like terms: 6a + -6a = 0
-11a + 2ax = 0 + 3ax
-11a + 2ax = 3ax

Add '-3ax' to each side of the equation.
-11a + 2ax + -3ax = 3ax + -3ax

Combine like terms: 2ax + -3ax = -1ax
-11a + -1ax = 3ax + -3ax

Combine like terms: 3ax + -3ax = 0
-11a + -1ax = 0

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(11 + x) = 0

Ignore the factor -1.
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 '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Add '-1x' to each side of the equation.
x + -1x = -11 + -1x

Combine like terms: x + -1x = 0
0 = -11 + -1x

Simplifying
0 = -11 + -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}