0=x^4+2x^3+15x^2

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Solution for 0=x^4+2x^3+15x^2 equation: 


Simplifying
0 = x4 + 2x3 + 15x2

Reorder the terms:
0 = 15x2 + 2x3 + x4

Solving
0 = 15x2 + 2x3 + x4

Solving for variable 'x'.
Remove the zero:
-15x2 + -2x3 + -1x4 = 15x2 + 2x3 + x4 + -15x2 + -2x3 + -1x4

Reorder the terms:
-15x2 + -2x3 + -1x4 = 15x2 + -15x2 + 2x3 + -2x3 + x4 + -1x4

Combine like terms: 15x2 + -15x2 = 0
-15x2 + -2x3 + -1x4 = 0 + 2x3 + -2x3 + x4 + -1x4
-15x2 + -2x3 + -1x4 = 2x3 + -2x3 + x4 + -1x4

Combine like terms: 2x3 + -2x3 = 0
-15x2 + -2x3 + -1x4 = 0 + x4 + -1x4
-15x2 + -2x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-15x2 + -2x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1x2'.
-1x2(15 + 2x + x2) = 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 '(15 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 2x + x2 = 0

Solving
15 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 2x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 2x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2x + x2 = 0 + -15
2x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
2x + x2 = -15

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -15 + 1

Reorder the terms:
1 + 2x + x2 = -15 + 1

Combine like terms: -15 + 1 = -14
1 + 2x + x2 = -14

Factor a perfect square on the left side:
(x + 1)(x + 1) = -14

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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