-5=x^3-9x^2+24x-5

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Solution for -5=x^3-9x^2+24x-5 equation: 


Simplifying
-5 = x3 + -9x2 + 24x + -5

Reorder the terms:
-5 = -5 + 24x + -9x2 + x3

Add '5' to each side of the equation.
-5 + 5 = -5 + 24x + -9x2 + 5 + x3

Combine like terms: -5 + 5 = 0
0 = -5 + 24x + -9x2 + 5 + x3

Reorder the terms:
0 = -5 + 5 + 24x + -9x2 + x3

Combine like terms: -5 + 5 = 0
0 = 0 + 24x + -9x2 + x3
0 = 24x + -9x2 + x3

Solving
0 = 24x + -9x2 + x3

Solving for variable 'x'.
Remove the zero:
-24x + 9x2 + -1x3 = 24x + -9x2 + x3 + -24x + 9x2 + -1x3

Reorder the terms:
-24x + 9x2 + -1x3 = 24x + -24x + -9x2 + 9x2 + x3 + -1x3

Combine like terms: 24x + -24x = 0
-24x + 9x2 + -1x3 = 0 + -9x2 + 9x2 + x3 + -1x3
-24x + 9x2 + -1x3 = -9x2 + 9x2 + x3 + -1x3

Combine like terms: -9x2 + 9x2 = 0
-24x + 9x2 + -1x3 = 0 + x3 + -1x3
-24x + 9x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-24x + 9x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + 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 '(-24 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
-24 + 9x + -1x2 = 0

Solving
-24 + 9x + -1x2 = 0

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

Divide each side by '-1'.
24 + -9x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -9x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -9x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -9x + x2 = 0 + -24
-9x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-9x + x2 = -24

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 = -24 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -24 + 20.25

Combine like terms: -24 + 20.25 = -3.75
20.25 + -9x + x2 = -3.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = -3.75

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}

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