0=2x^4+14x^3+24x^2

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Solution for 0=2x^4+14x^3+24x^2 equation: 


Simplifying
0 = 2x4 + 14x3 + 24x2

Reorder the terms:
0 = 24x2 + 14x3 + 2x4

Solving
0 = 24x2 + 14x3 + 2x4

Solving for variable 'x'.
Remove the zero:
-24x2 + -14x3 + -2x4 = 24x2 + 14x3 + 2x4 + -24x2 + -14x3 + -2x4

Reorder the terms:
-24x2 + -14x3 + -2x4 = 24x2 + -24x2 + 14x3 + -14x3 + 2x4 + -2x4

Combine like terms: 24x2 + -24x2 = 0
-24x2 + -14x3 + -2x4 = 0 + 14x3 + -14x3 + 2x4 + -2x4
-24x2 + -14x3 + -2x4 = 14x3 + -14x3 + 2x4 + -2x4

Combine like terms: 14x3 + -14x3 = 0
-24x2 + -14x3 + -2x4 = 0 + 2x4 + -2x4
-24x2 + -14x3 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
-24x2 + -14x3 + -2x4 = 0

Factor out the Greatest Common Factor (GCF), '-2x2'.
-2x2(12 + 7x + x2) = 0

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

Ignore the factor -2.

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 '(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
Solution
x = {0, -4, -3}

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