3x^3(7x^2+x-3)=

Solution for 3x^3(7x^2+x-3)= equation:

Simplifying
3x3(7x2 + x + -3) = 0

Reorder the terms:
3x3(-3 + x + 7x2) = 0
(-3 * 3x3 + x * 3x3 + 7x2 * 3x3) = 0
(-9x3 + 3x4 + 21x5) = 0

Solving
-9x3 + 3x4 + 21x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(-3 + x + 7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + x + 7x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + 7x2 = 0

Solving
-3 + x + 7x2 = 0

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

Divide each side by '7'.
-0.4285714286 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.1428571429x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.1428571429x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.1428571429x + x2 = 0 + 0.4285714286
0.1428571429x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.1428571429x + x2 = 0.4285714286

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1428571429x + 0.25 + x2 = 0.4285714286 + 0.25

Reorder the terms:
0.25 + 0.1428571429x + x2 = 0.4285714286 + 0.25

Combine like terms: 0.4285714286 + 0.25 = 0.6785714286
0.25 + 0.1428571429x + x2 = 0.6785714286

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.6785714286

Calculate the square root of the right side: 0.823754471

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.823754471 and -0.823754471.

Subproblem 1
x + 0.5 = 0.823754471

Simplifying
x + 0.5 = 0.823754471

Reorder the terms:
0.5 + x = 0.823754471

Solving
0.5 + x = 0.823754471

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.823754471 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.823754471 + -0.5
x = 0.823754471 + -0.5

Combine like terms: 0.823754471 + -0.5 = 0.323754471
x = 0.323754471

Simplifying
x = 0.323754471

Subproblem 2
x + 0.5 = -0.823754471

Simplifying
x + 0.5 = -0.823754471

Reorder the terms:
0.5 + x = -0.823754471

Solving
0.5 + x = -0.823754471

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.823754471 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.823754471 + -0.5
x = -0.823754471 + -0.5

Combine like terms: -0.823754471 + -0.5 = -1.323754471
x = -1.323754471

Simplifying
x = -1.323754471

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.323754471, -1.323754471}
Solution
x = {0.323754471, -1.323754471}