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

Solution for 0=a(x+2)(x-1)(x-3) equation:

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

Reorder the terms:
0 = a(2 + x)(x + -1)(x + -3)

Reorder the terms:
0 = a(2 + x)(-1 + x)(x + -3)

Reorder the terms:
0 = a(2 + x)(-1 + x)(-3 + x)

Multiply (2 + x) * (-1 + x)
0 = a(2(-1 + x) + x(-1 + x))(-3 + x)
0 = a((-1 * 2 + x * 2) + x(-1 + x))(-3 + x)
0 = a((-2 + 2x) + x(-1 + x))(-3 + x)
0 = a(-2 + 2x + (-1 * x + x * x))(-3 + x)
0 = a(-2 + 2x + (-1x + x2))(-3 + x)

Combine like terms: 2x + -1x = 1x
0 = a(-2 + 1x + x2)(-3 + x)

Multiply (-2 + 1x + x2) * (-3 + x)
0 = a(-2(-3 + x) + 1x * (-3 + x) + x2(-3 + x))
0 = a((-3 * -2 + x * -2) + 1x * (-3 + x) + x2(-3 + x))
0 = a((6 + -2x) + 1x * (-3 + x) + x2(-3 + x))
0 = a(6 + -2x + (-3 * 1x + x * 1x) + x2(-3 + x))
0 = a(6 + -2x + (-3x + 1x2) + x2(-3 + x))
0 = a(6 + -2x + -3x + 1x2 + (-3 * x2 + x * x2))
0 = a(6 + -2x + -3x + 1x2 + (-3x2 + x3))

Combine like terms: -2x + -3x = -5x
0 = a(6 + -5x + 1x2 + -3x2 + x3)

Combine like terms: 1x2 + -3x2 = -2x2
0 = a(6 + -5x + -2x2 + x3)
0 = (6 * a + -5x * a + -2x2 * a + x3 * a)
0 = (6a + -5ax + -2ax2 + ax3)

Solving
0 = 6a + -5ax + -2ax2 + ax3

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.
0 + -6a = 6a + -5ax + -2ax2 + -6a + ax3
Remove the zero:
-6a = 6a + -5ax + -2ax2 + -6a + ax3

Reorder the terms:
-6a = 6a + -6a + -5ax + -2ax2 + ax3

Combine like terms: 6a + -6a = 0
-6a = 0 + -5ax + -2ax2 + ax3
-6a = -5ax + -2ax2 + ax3

Add '5ax' to each side of the equation.
-6a + 5ax = -5ax + -2ax2 + 5ax + ax3

Reorder the terms:
-6a + 5ax = -5ax + 5ax + -2ax2 + ax3

Combine like terms: -5ax + 5ax = 0
-6a + 5ax = 0 + -2ax2 + ax3
-6a + 5ax = -2ax2 + ax3

Add '2ax2' to each side of the equation.
-6a + 5ax + 2ax2 = -2ax2 + 2ax2 + ax3

Combine like terms: -2ax2 + 2ax2 = 0
-6a + 5ax + 2ax2 = 0 + ax3
-6a + 5ax + 2ax2 = ax3

Add '-1ax3' to each side of the equation.
-6a + 5ax + 2ax2 + -1ax3 = ax3 + -1ax3

Combine like terms: ax3 + -1ax3 = 0
-6a + 5ax + 2ax2 + -1ax3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-6 + 5x + 2x2 + -1x3) = 0

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 '(-6 + 5x + 2x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-6 + 5x + 2x2 + -1x3 = 0

Solving
-6 + 5x + 2x2 + -1x3 = 0

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

Add '6' to each side of the equation.
-6 + 5x + 2x2 + 6 + -1x3 = 0 + 6

Reorder the terms:
-6 + 6 + 5x + 2x2 + -1x3 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 5x + 2x2 + -1x3 = 0 + 6
5x + 2x2 + -1x3 = 0 + 6

Combine like terms: 0 + 6 = 6
5x + 2x2 + -1x3 = 6

Add '-5x' to each side of the equation.
5x + 2x2 + -5x + -1x3 = 6 + -5x

Reorder the terms:
5x + -5x + 2x2 + -1x3 = 6 + -5x

Combine like terms: 5x + -5x = 0
0 + 2x2 + -1x3 = 6 + -5x
2x2 + -1x3 = 6 + -5x

Add '-2x2' to each side of the equation.
2x2 + -2x2 + -1x3 = 6 + -5x + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1x3 = 6 + -5x + -2x2
-1x3 = 6 + -5x + -2x2

Add 'x3' to each side of the equation.
-1x3 + x3 = 6 + -5x + -2x2 + x3

Combine like terms: -1x3 + x3 = 0
0 = 6 + -5x + -2x2 + x3

Simplifying
0 = 6 + -5x + -2x2 + x3

The solution to this equation could not be determined.

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