8=-5(4x+3)211x

Solution for 8=-5(4x+3)211x equation:

Simplifying
8 = -5(4x + 3) * 211x

Reorder the terms:
8 = -5(3 + 4x) * 211x

Reorder the terms for easier multiplication:
8 = -5 * 211x(3 + 4x)

Multiply -5 * 211
8 = -1055x(3 + 4x)
8 = (3 * -1055x + 4x * -1055x)
8 = (-3165x + -4220x2)

Solving
8 = -3165x + -4220x2

Solving for variable 'x'.

Reorder the terms:
8 + 3165x + 4220x2 = -3165x + 3165x + -4220x2 + 4220x2

Combine like terms: -3165x + 3165x = 0
8 + 3165x + 4220x2 = 0 + -4220x2 + 4220x2
8 + 3165x + 4220x2 = -4220x2 + 4220x2

Combine like terms: -4220x2 + 4220x2 = 0
8 + 3165x + 4220x2 = 0

Begin completing the square.  Divide all terms by
4220 the coefficient of the squared term: 

Divide each side by '4220'.
0.001895734597 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.001895734597' to each side of the equation.
0.001895734597 + 0.75x + -0.001895734597 + x2 = 0 + -0.001895734597

Reorder the terms:
0.001895734597 + -0.001895734597 + 0.75x + x2 = 0 + -0.001895734597

Combine like terms: 0.001895734597 + -0.001895734597 = 0.000000000000
0.000000000000 + 0.75x + x2 = 0 + -0.001895734597
0.75x + x2 = 0 + -0.001895734597

Combine like terms: 0 + -0.001895734597 = -0.001895734597
0.75x + x2 = -0.001895734597

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.001895734597 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.001895734597 + 0.140625

Combine like terms: -0.001895734597 + 0.140625 = 0.138729265403
0.140625 + 0.75x + x2 = 0.138729265403

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.138729265403

Calculate the square root of the right side: 0.372463777

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.372463777 and -0.372463777.

Subproblem 1
x + 0.375 = 0.372463777

Simplifying
x + 0.375 = 0.372463777

Reorder the terms:
0.375 + x = 0.372463777

Solving
0.375 + x = 0.372463777

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.372463777 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.372463777 + -0.375
x = 0.372463777 + -0.375

Combine like terms: 0.372463777 + -0.375 = -0.002536223
x = -0.002536223

Simplifying
x = -0.002536223

Subproblem 2
x + 0.375 = -0.372463777

Simplifying
x + 0.375 = -0.372463777

Reorder the terms:
0.375 + x = -0.372463777

Solving
0.375 + x = -0.372463777

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.372463777 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.372463777 + -0.375
x = -0.372463777 + -0.375

Combine like terms: -0.372463777 + -0.375 = -0.747463777
x = -0.747463777

Simplifying
x = -0.747463777

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.002536223, -0.747463777}