=21x^4+18x^2+36x^3

Solution for =21x^4+18x^2+36x^3 equation:

Simplifying
0 = 21x4 + 18x2 + 36x3

Reorder the terms:
0 = 18x2 + 36x3 + 21x4

Solving
0 = 18x2 + 36x3 + 21x4

Solving for variable 'x'.
Remove the zero:
-18x2 + -36x3 + -21x4 = 18x2 + 36x3 + 21x4 + -18x2 + -36x3 + -21x4

Reorder the terms:
-18x2 + -36x3 + -21x4 = 18x2 + -18x2 + 36x3 + -36x3 + 21x4 + -21x4

Combine like terms: 18x2 + -18x2 = 0
-18x2 + -36x3 + -21x4 = 0 + 36x3 + -36x3 + 21x4 + -21x4
-18x2 + -36x3 + -21x4 = 36x3 + -36x3 + 21x4 + -21x4

Combine like terms: 36x3 + -36x3 = 0
-18x2 + -36x3 + -21x4 = 0 + 21x4 + -21x4
-18x2 + -36x3 + -21x4 = 21x4 + -21x4

Combine like terms: 21x4 + -21x4 = 0
-18x2 + -36x3 + -21x4 = 0

Factor out the Greatest Common Factor (GCF), '-3x2'.
-3x2(6 + 12x + 7x2) = 0

Ignore the factor -3.
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 '(6 + 12x + 7x2)' equal to zero and attempt to solve:

Simplifying
6 + 12x + 7x2 = 0

Solving
6 + 12x + 7x2 = 0

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

Divide each side by '7'.
0.8571428571 + 1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 1.714285714x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 1.714285714x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 1.714285714x + x2 = 0 + -0.8571428571
1.714285714x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
1.714285714x + x2 = -0.8571428571

The x term is 1.714285714x.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714x + 0.7346938773 + x2 = -0.8571428571 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714x + x2 = -0.8571428571 + 0.7346938773

Combine like terms: -0.8571428571 + 0.7346938773 = -0.1224489798
0.7346938773 + 1.714285714x + x2 = -0.1224489798

Factor a perfect square on the left side:
(x + 0.857142857)(x + 0.857142857) = -0.1224489798

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}