(3-x)(3-x)(3-x)-1=26

Solution for (3-x)(3-x)(3-x)-1=26 equation:

Simplifying
(3 + -1x)(3 + -1x)(3 + -1x) + -1 = 26

Multiply (3 + -1x) * (3 + -1x)
(3(3 + -1x) + -1x * (3 + -1x))(3 + -1x) + -1 = 26
((3 * 3 + -1x * 3) + -1x * (3 + -1x))(3 + -1x) + -1 = 26
((9 + -3x) + -1x * (3 + -1x))(3 + -1x) + -1 = 26
(9 + -3x + (3 * -1x + -1x * -1x))(3 + -1x) + -1 = 26
(9 + -3x + (-3x + 1x2))(3 + -1x) + -1 = 26

Combine like terms: -3x + -3x = -6x
(9 + -6x + 1x2)(3 + -1x) + -1 = 26

Multiply (9 + -6x + 1x2) * (3 + -1x)
(9(3 + -1x) + -6x * (3 + -1x) + 1x2 * (3 + -1x)) + -1 = 26
((3 * 9 + -1x * 9) + -6x * (3 + -1x) + 1x2 * (3 + -1x)) + -1 = 26
((27 + -9x) + -6x * (3 + -1x) + 1x2 * (3 + -1x)) + -1 = 26
(27 + -9x + (3 * -6x + -1x * -6x) + 1x2 * (3 + -1x)) + -1 = 26
(27 + -9x + (-18x + 6x2) + 1x2 * (3 + -1x)) + -1 = 26
(27 + -9x + -18x + 6x2 + (3 * 1x2 + -1x * 1x2)) + -1 = 26
(27 + -9x + -18x + 6x2 + (3x2 + -1x3)) + -1 = 26

Combine like terms: -9x + -18x = -27x
(27 + -27x + 6x2 + 3x2 + -1x3) + -1 = 26

Combine like terms: 6x2 + 3x2 = 9x2
(27 + -27x + 9x2 + -1x3) + -1 = 26

Reorder the terms:
27 + -1 + -27x + 9x2 + -1x3 = 26

Combine like terms: 27 + -1 = 26
26 + -27x + 9x2 + -1x3 = 26

Add '-26' to each side of the equation.
26 + -27x + 9x2 + -26 + -1x3 = 26 + -26

Reorder the terms:
26 + -26 + -27x + 9x2 + -1x3 = 26 + -26

Combine like terms: 26 + -26 = 0
0 + -27x + 9x2 + -1x3 = 26 + -26
-27x + 9x2 + -1x3 = 26 + -26

Combine like terms: 26 + -26 = 0
-27x + 9x2 + -1x3 = 0

Solving
-27x + 9x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-27 + 9x + -1x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-27 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
-27 + 9x + -1x2 = 0

Solving
-27 + 9x + -1x2 = 0

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

Divide each side by '-1'.
27 + -9x + x2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -9x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -9x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -9x + x2 = 0 + -27
-9x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-9x + x2 = -27

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -27 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -27 + 20.25

Combine like terms: -27 + 20.25 = -6.75
20.25 + -9x + x2 = -6.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = -6.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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