0=5x^3+16x^2+3x

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Solution for 0=5x^3+16x^2+3x equation: 


Simplifying
0 = 5x3 + 16x2 + 3x

Reorder the terms:
0 = 3x + 16x2 + 5x3

Solving
0 = 3x + 16x2 + 5x3

Solving for variable 'x'.
Remove the zero:
-3x + -16x2 + -5x3 = 3x + 16x2 + 5x3 + -3x + -16x2 + -5x3

Reorder the terms:
-3x + -16x2 + -5x3 = 3x + -3x + 16x2 + -16x2 + 5x3 + -5x3

Combine like terms: 3x + -3x = 0
-3x + -16x2 + -5x3 = 0 + 16x2 + -16x2 + 5x3 + -5x3
-3x + -16x2 + -5x3 = 16x2 + -16x2 + 5x3 + -5x3

Combine like terms: 16x2 + -16x2 = 0
-3x + -16x2 + -5x3 = 0 + 5x3 + -5x3
-3x + -16x2 + -5x3 = 5x3 + -5x3

Combine like terms: 5x3 + -5x3 = 0
-3x + -16x2 + -5x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(3 + 16x + 5x2) = 0

Factor a trinomial.
-1x((3 + x)(1 + 5x)) = 0

Ignore the factor -1.

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

Subproblem 3
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {0, -3, -0.2}

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