x^3+3x^2-8x=0

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Solution for x^3+3x^2-8x=0 equation: 


Simplifying
x3 + 3x2 + -8x = 0

Reorder the terms:
-8x + 3x2 + x3 = 0

Solving
-8x + 3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 3x + x2) = 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 '(-8 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 3x + x2 = 0

Solving
-8 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 3x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x + x2 = 0 + 8
3x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
3x + x2 = 8

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 = 8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3x + x2 = 10.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 1.5 = 3.201562119

Simplifying
x + 1.5 = 3.201562119

Reorder the terms:
1.5 + x = 3.201562119

Solving
1.5 + x = 3.201562119

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 = 3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.201562119 + -1.5
x = 3.201562119 + -1.5

Combine like terms: 3.201562119 + -1.5 = 1.701562119
x = 1.701562119

Simplifying
x = 1.701562119


Subproblem 2
x + 1.5 = -3.201562119

Simplifying
x + 1.5 = -3.201562119

Reorder the terms:
1.5 + x = -3.201562119

Solving
1.5 + x = -3.201562119

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 = -3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.201562119 + -1.5
x = -3.201562119 + -1.5

Combine like terms: -3.201562119 + -1.5 = -4.701562119
x = -4.701562119

Simplifying
x = -4.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.701562119, -4.701562119}
Solution
x = {0, 1.701562119, -4.701562119}

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