(x+1)3-(x-1)3=6x(x-3)

Solution for (x+1)3-(x-1)3=6x(x-3) equation:

Simplifying
(x + 1) * 3 + -1(x + -1) * 3 = 6x(x + -3)

Reorder the terms:
(1 + x) * 3 + -1(x + -1) * 3 = 6x(x + -3)

Reorder the terms for easier multiplication:
3(1 + x) + -1(x + -1) * 3 = 6x(x + -3)
(1 * 3 + x * 3) + -1(x + -1) * 3 = 6x(x + -3)
(3 + 3x) + -1(x + -1) * 3 = 6x(x + -3)

Reorder the terms:
3 + 3x + -1(-1 + x) * 3 = 6x(x + -3)

Reorder the terms for easier multiplication:
3 + 3x + -1 * 3(-1 + x) = 6x(x + -3)

Multiply -1 * 3
3 + 3x + -3(-1 + x) = 6x(x + -3)
3 + 3x + (-1 * -3 + x * -3) = 6x(x + -3)
3 + 3x + (3 + -3x) = 6x(x + -3)

Reorder the terms:
3 + 3 + 3x + -3x = 6x(x + -3)

Combine like terms: 3 + 3 = 6
6 + 3x + -3x = 6x(x + -3)

Combine like terms: 3x + -3x = 0
6 + 0 = 6x(x + -3)
6 = 6x(x + -3)

Reorder the terms:
6 = 6x(-3 + x)
6 = (-3 * 6x + x * 6x)
6 = (-18x + 6x2)

Solving
6 = -18x + 6x2

Solving for variable 'x'.

Reorder the terms:
6 + 18x + -6x2 = -18x + 18x + 6x2 + -6x2

Combine like terms: -18x + 18x = 0
6 + 18x + -6x2 = 0 + 6x2 + -6x2
6 + 18x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
6 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x + -1x2 = 0

Solving
1 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -3x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638

Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}
Solution
x = {3.302775638, -0.302775638}