x(x^2+5x+15x+10)=0

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Solution for x(x^2+5x+15x+10)=0 equation: 


Simplifying
x(x2 + 5x + 15x + 10) = 0

Reorder the terms:
x(10 + 5x + 15x + x2) = 0

Combine like terms: 5x + 15x = 20x
x(10 + 20x + x2) = 0
(10 * x + 20x * x + x2 * x) = 0
(10x + 20x2 + x3) = 0

Solving
10x + 20x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + 20x + x2) = 0


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 '(10 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 20x + x2 = 0

Solving
10 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 20x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 20x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 20x + x2 = 0 + -10
20x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
20x + x2 = -10

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -10 + 100

Reorder the terms:
100 + 20x + x2 = -10 + 100

Combine like terms: -10 + 100 = 90
100 + 20x + x2 = 90

Factor a perfect square on the left side:
(x + 10)(x + 10) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + 10) equal to 9.486832981 and -9.486832981.


Subproblem 1
x + 10 = 9.486832981

Simplifying
x + 10 = 9.486832981

Reorder the terms:
10 + x = 9.486832981

Solving
10 + x = 9.486832981

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.486832981 + -10
x = 9.486832981 + -10

Combine like terms: 9.486832981 + -10 = -0.513167019
x = -0.513167019

Simplifying
x = -0.513167019


Subproblem 2
x + 10 = -9.486832981

Simplifying
x + 10 = -9.486832981

Reorder the terms:
10 + x = -9.486832981

Solving
10 + x = -9.486832981

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.486832981 + -10
x = -9.486832981 + -10

Combine like terms: -9.486832981 + -10 = -19.486832981
x = -19.486832981

Simplifying
x = -19.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.513167019, -19.486832981}
Solution
x = {0, -0.513167019, -19.486832981}

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