-3a(5x-1)+a(5-2x)-3a(x+1)=

Solution for -3a(5x-1)+a(5-2x)-3a(x+1)= equation:

Simplifying
-3a(5x + -1) + a(5 + -2x) + -3a(x + 1) = 0

Reorder the terms:
-3a(-1 + 5x) + a(5 + -2x) + -3a(x + 1) = 0
(-1 * -3a + 5x * -3a) + a(5 + -2x) + -3a(x + 1) = 0
(3a + -15ax) + a(5 + -2x) + -3a(x + 1) = 0
3a + -15ax + (5 * a + -2x * a) + -3a(x + 1) = 0
3a + -15ax + (5a + -2ax) + -3a(x + 1) = 0

Reorder the terms:
3a + -15ax + 5a + -2ax + -3a(1 + x) = 0
3a + -15ax + 5a + -2ax + (1 * -3a + x * -3a) = 0
3a + -15ax + 5a + -2ax + (-3a + -3ax) = 0

Reorder the terms:
3a + 5a + -3a + -15ax + -2ax + -3ax = 0

Combine like terms: 3a + 5a = 8a
8a + -3a + -15ax + -2ax + -3ax = 0

Combine like terms: 8a + -3a = 5a
5a + -15ax + -2ax + -3ax = 0

Combine like terms: -15ax + -2ax = -17ax
5a + -17ax + -3ax = 0

Combine like terms: -17ax + -3ax = -20ax
5a + -20ax = 0

Solving
5a + -20ax = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '5a'.
5a(1 + -4x) = 0

Ignore the factor 5.
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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 4x

The solution to this equation could not be determined.

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