8*(x+10+2x+4)*x+8+-6=

Solution for 8*(x+10+2x+4)*x+8+-6= equation:

Simplifying
8(x + 10 + 2x + 4) * x + 8 + -6 = 0

Reorder the terms:
8(10 + 4 + x + 2x) * x + 8 + -6 = 0

Combine like terms: 10 + 4 = 14
8(14 + x + 2x) * x + 8 + -6 = 0

Combine like terms: x + 2x = 3x
8(14 + 3x) * x + 8 + -6 = 0

Reorder the terms for easier multiplication:
8x(14 + 3x) + 8 + -6 = 0
(14 * 8x + 3x * 8x) + 8 + -6 = 0
(112x + 24x2) + 8 + -6 = 0

Reorder the terms:
8 + -6 + 112x + 24x2 = 0

Combine like terms: 8 + -6 = 2
2 + 112x + 24x2 = 0

Solving
2 + 112x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 56x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 56x + 12x2)' equal to zero and attempt to solve:

Simplifying
1 + 56x + 12x2 = 0

Solving
1 + 56x + 12x2 = 0

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

Divide each side by '12'.
0.08333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + 4.666666667x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + 4.666666667x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + 4.666666667x + x2 = 0 + -0.08333333333
4.666666667x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
4.666666667x + x2 = -0.08333333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -0.08333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -0.08333333333 + 5.444444448

Combine like terms: -0.08333333333 + 5.444444448 = 5.36111111467
5.444444448 + 4.666666667x + x2 = 5.36111111467

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 5.36111111467

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.315407332 and -2.315407332.

Subproblem 1
x + 2.333333334 = 2.315407332

Simplifying
x + 2.333333334 = 2.315407332

Reorder the terms:
2.333333334 + x = 2.315407332

Solving
2.333333334 + x = 2.315407332

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 2.315407332 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.315407332 + -2.333333334
x = 2.315407332 + -2.333333334

Combine like terms: 2.315407332 + -2.333333334 = -0.017926002
x = -0.017926002

Simplifying
x = -0.017926002

Subproblem 2
x + 2.333333334 = -2.315407332

Simplifying
x + 2.333333334 = -2.315407332

Reorder the terms:
2.333333334 + x = -2.315407332

Solving
2.333333334 + x = -2.315407332

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -2.315407332 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.315407332 + -2.333333334
x = -2.315407332 + -2.333333334

Combine like terms: -2.315407332 + -2.333333334 = -4.648740666
x = -4.648740666

Simplifying
x = -4.648740666

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.017926002, -4.648740666}
Solution
x = {-0.017926002, -4.648740666}