=16x^3+12x^2+8x

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Solution for =16x^3+12x^2+8x equation: 


Simplifying
0 = 16x3 + 12x2 + 8x

Reorder the terms:
0 = 8x + 12x2 + 16x3

Solving
0 = 8x + 12x2 + 16x3

Solving for variable 'x'.
Remove the zero:
-8x + -12x2 + -16x3 = 8x + 12x2 + 16x3 + -8x + -12x2 + -16x3

Reorder the terms:
-8x + -12x2 + -16x3 = 8x + -8x + 12x2 + -12x2 + 16x3 + -16x3

Combine like terms: 8x + -8x = 0
-8x + -12x2 + -16x3 = 0 + 12x2 + -12x2 + 16x3 + -16x3
-8x + -12x2 + -16x3 = 12x2 + -12x2 + 16x3 + -16x3

Combine like terms: 12x2 + -12x2 = 0
-8x + -12x2 + -16x3 = 0 + 16x3 + -16x3
-8x + -12x2 + -16x3 = 16x3 + -16x3

Combine like terms: 16x3 + -16x3 = 0
-8x + -12x2 + -16x3 = 0

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(2 + 3x + 4x2) = 0

Ignore the factor -4.

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 '(2 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x + 4x2 = 0

Solving
2 + 3x + 4x2 = 0

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

Divide each side by '4'.
0.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.75x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.75x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.75x + x2 = 0 + -0.5
0.75x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.75x + x2 = -0.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.5 + 0.140625

Combine like terms: -0.5 + 0.140625 = -0.359375
0.140625 + 0.75x + x2 = -0.359375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.359375

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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