0=3x^4+14x^3+8x^2

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Solution for 0=3x^4+14x^3+8x^2 equation: 


Simplifying
0 = 3x4 + 14x3 + 8x2

Reorder the terms:
0 = 8x2 + 14x3 + 3x4

Solving
0 = 8x2 + 14x3 + 3x4

Solving for variable 'x'.
Remove the zero:
-8x2 + -14x3 + -3x4 = 8x2 + 14x3 + 3x4 + -8x2 + -14x3 + -3x4

Reorder the terms:
-8x2 + -14x3 + -3x4 = 8x2 + -8x2 + 14x3 + -14x3 + 3x4 + -3x4

Combine like terms: 8x2 + -8x2 = 0
-8x2 + -14x3 + -3x4 = 0 + 14x3 + -14x3 + 3x4 + -3x4
-8x2 + -14x3 + -3x4 = 14x3 + -14x3 + 3x4 + -3x4

Combine like terms: 14x3 + -14x3 = 0
-8x2 + -14x3 + -3x4 = 0 + 3x4 + -3x4
-8x2 + -14x3 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-8x2 + -14x3 + -3x4 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(8 + 14x + 3x2) = 0

Factor a trinomial.
-1x2((4 + x)(2 + 3x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

Subproblem 3
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -4, -0.6666666667}

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