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

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


Simplifying
2x(3x + 5x + 2) + 4x(x2 + 6x) = 0

Reorder the terms:
2x(2 + 3x + 5x) + 4x(x2 + 6x) = 0

Combine like terms: 3x + 5x = 8x
2x(2 + 8x) + 4x(x2 + 6x) = 0
(2 * 2x + 8x * 2x) + 4x(x2 + 6x) = 0
(4x + 16x2) + 4x(x2 + 6x) = 0

Reorder the terms:
4x + 16x2 + 4x(6x + x2) = 0
4x + 16x2 + (6x * 4x + x2 * 4x) = 0
4x + 16x2 + (24x2 + 4x3) = 0

Combine like terms: 16x2 + 24x2 = 40x2
4x + 40x2 + 4x3 = 0

Solving
4x + 40x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + 10x + x2) = 0

Ignore the factor 4.

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 '(1 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 10x + x2 = 0

Solving
1 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 10x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 10x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10x + x2 = 0 + -1
10x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
10x + x2 = -1

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -1 + 25

Reorder the terms:
25 + 10x + x2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + 10x + x2 = 24

Factor a perfect square on the left side:
(x + 5)(x + 5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 5) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 5 = 4.898979486

Simplifying
x + 5 = 4.898979486

Reorder the terms:
5 + x = 4.898979486

Solving
5 + x = 4.898979486

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.898979486 + -5
x = 4.898979486 + -5

Combine like terms: 4.898979486 + -5 = -0.101020514
x = -0.101020514

Simplifying
x = -0.101020514


Subproblem 2
x + 5 = -4.898979486

Simplifying
x + 5 = -4.898979486

Reorder the terms:
5 + x = -4.898979486

Solving
5 + x = -4.898979486

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.898979486 + -5
x = -4.898979486 + -5

Combine like terms: -4.898979486 + -5 = -9.898979486
x = -9.898979486

Simplifying
x = -9.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.101020514, -9.898979486}
Solution
x = {0, -0.101020514, -9.898979486}

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