5x(x^2+156x-400)=0

Solution for 5x(x^2+156x-400)=0 equation:

Simplifying
5x(x2 + 156x + -400) = 0

Reorder the terms:
5x(-400 + 156x + x2) = 0
(-400 * 5x + 156x * 5x + x2 * 5x) = 0
(-2000x + 780x2 + 5x3) = 0

Solving
-2000x + 780x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-400 + 156x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-400 + 156x + x2)' equal to zero and attempt to solve:

Simplifying
-400 + 156x + x2 = 0

Solving
-400 + 156x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 156x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 156x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 156x + x2 = 0 + 400
156x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
156x + x2 = 400

The x term is 156x.  Take half its coefficient (78).
Square it (6084) and add it to both sides.

Add '6084' to each side of the equation.
156x + 6084 + x2 = 400 + 6084

Reorder the terms:
6084 + 156x + x2 = 400 + 6084

Combine like terms: 400 + 6084 = 6484
6084 + 156x + x2 = 6484

Factor a perfect square on the left side:
(x + 78)(x + 78) = 6484

Calculate the square root of the right side: 80.523288557

Break this problem into two subproblems by setting 
(x + 78) equal to 80.523288557 and -80.523288557.

Subproblem 1
x + 78 = 80.523288557

Simplifying
x + 78 = 80.523288557

Reorder the terms:
78 + x = 80.523288557

Solving
78 + x = 80.523288557

Solving for variable 'x'.

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

Add '-78' to each side of the equation.
78 + -78 + x = 80.523288557 + -78

Combine like terms: 78 + -78 = 0
0 + x = 80.523288557 + -78
x = 80.523288557 + -78

Combine like terms: 80.523288557 + -78 = 2.523288557
x = 2.523288557

Simplifying
x = 2.523288557

Subproblem 2
x + 78 = -80.523288557

Simplifying
x + 78 = -80.523288557

Reorder the terms:
78 + x = -80.523288557

Solving
78 + x = -80.523288557

Solving for variable 'x'.

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

Add '-78' to each side of the equation.
78 + -78 + x = -80.523288557 + -78

Combine like terms: 78 + -78 = 0
0 + x = -80.523288557 + -78
x = -80.523288557 + -78

Combine like terms: -80.523288557 + -78 = -158.523288557
x = -158.523288557

Simplifying
x = -158.523288557

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.523288557, -158.523288557}
Solution
x = {0, 2.523288557, -158.523288557}