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

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


Simplifying
2x3 + 3x2 + 8x = 0

Reorder the terms:
8x + 3x2 + 2x3 = 0

Solving
8x + 3x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 3x + 2x2) = 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 + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + 3x + 2x2 = 0

Solving
8 + 3x + 2x2 = 0

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

Divide each side by '2'.
4 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 1.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 1.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 1.5x + x2 = 0 + -4
1.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
1.5x + x2 = -4

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -4 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -4 + 0.5625

Combine like terms: -4 + 0.5625 = -3.4375
0.5625 + 1.5x + x2 = -3.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -3.4375

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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