a(x^3+1)+3ax(x+1)=

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Solution for a(x^3+1)+3ax(x+1)= equation: 


Simplifying
a(x3 + 1) + 3ax(x + 1) = 0

Reorder the terms:
a(1 + x3) + 3ax(x + 1) = 0
(1 * a + x3 * a) + 3ax(x + 1) = 0
(1a + ax3) + 3ax(x + 1) = 0

Reorder the terms:
1a + ax3 + 3ax(1 + x) = 0
1a + ax3 + (1 * 3ax + x * 3ax) = 0
1a + ax3 + (3ax + 3ax2) = 0

Reorder the terms:
1a + 3ax + 3ax2 + ax3 = 0

Solving
1a + 3ax + 3ax2 + ax3 = 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), 'a'.
a(1 + 3x + 3x2 + x3) = 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 '(1 + 3x + 3x2 + x3)' equal to zero and attempt to solve:

Simplifying
1 + 3x + 3x2 + x3 = 0

Solving
1 + 3x + 3x2 + x3 = 0

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

Add '-1' to each side of the equation.
1 + 3x + 3x2 + -1 + x3 = 0 + -1

Reorder the terms:
1 + -1 + 3x + 3x2 + x3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + 3x2 + x3 = 0 + -1
3x + 3x2 + x3 = 0 + -1

Combine like terms: 0 + -1 = -1
3x + 3x2 + x3 = -1

Add '-3x' to each side of the equation.
3x + 3x2 + -3x + x3 = -1 + -3x

Reorder the terms:
3x + -3x + 3x2 + x3 = -1 + -3x

Combine like terms: 3x + -3x = 0
0 + 3x2 + x3 = -1 + -3x
3x2 + x3 = -1 + -3x

Add '-3x2' to each side of the equation.
3x2 + -3x2 + x3 = -1 + -3x + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + x3 = -1 + -3x + -3x2
x3 = -1 + -3x + -3x2

Add '-1x3' to each side of the equation.
x3 + -1x3 = -1 + -3x + -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = -1 + -3x + -3x2 + -1x3

Simplifying
0 = -1 + -3x + -3x2 + -1x3

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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