2x^3(5x^2+4x-6)=

Solution for 2x^3(5x^2+4x-6)= equation:

Simplifying
2x3(5x2 + 4x + -6) = 0

Reorder the terms:
2x3(-6 + 4x + 5x2) = 0
(-6 * 2x3 + 4x * 2x3 + 5x2 * 2x3) = 0
(-12x3 + 8x4 + 10x5) = 0

Solving
-12x3 + 8x4 + 10x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x3'.
2x3(-6 + 4x + 5x2) = 0

Ignore the factor 2.
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 '(-6 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 4x + 5x2 = 0

Solving
-6 + 4x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + 0.8x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.8x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.8x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.8x + x2 = 0 + 1.2
0.8x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
0.8x + x2 = 1.2

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1.2 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1.2 + 0.16

Combine like terms: 1.2 + 0.16 = 1.36
0.16 + 0.8x + x2 = 1.36

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.166190379 and -1.166190379.

Subproblem 1
x + 0.4 = 1.166190379

Simplifying
x + 0.4 = 1.166190379

Reorder the terms:
0.4 + x = 1.166190379

Solving
0.4 + x = 1.166190379

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.166190379 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.166190379 + -0.4
x = 1.166190379 + -0.4

Combine like terms: 1.166190379 + -0.4 = 0.766190379
x = 0.766190379

Simplifying
x = 0.766190379

Subproblem 2
x + 0.4 = -1.166190379

Simplifying
x + 0.4 = -1.166190379

Reorder the terms:
0.4 + x = -1.166190379

Solving
0.4 + x = -1.166190379

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.166190379 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.166190379 + -0.4
x = -1.166190379 + -0.4

Combine like terms: -1.166190379 + -0.4 = -1.566190379
x = -1.566190379

Simplifying
x = -1.566190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.766190379, -1.566190379}
Solution
x = {0.766190379, -1.566190379}