8=-5(4x+3)21x

Solution for 8=-5(4x+3)21x equation:

Simplifying
8 = -5(4x + 3) * 21x

Reorder the terms:
8 = -5(3 + 4x) * 21x

Reorder the terms for easier multiplication:
8 = -5 * 21x(3 + 4x)

Multiply -5 * 21
8 = -105x(3 + 4x)
8 = (3 * -105x + 4x * -105x)
8 = (-315x + -420x2)

Solving
8 = -315x + -420x2

Solving for variable 'x'.

Reorder the terms:
8 + 315x + 420x2 = -315x + 315x + -420x2 + 420x2

Combine like terms: -315x + 315x = 0
8 + 315x + 420x2 = 0 + -420x2 + 420x2
8 + 315x + 420x2 = -420x2 + 420x2

Combine like terms: -420x2 + 420x2 = 0
8 + 315x + 420x2 = 0

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

Divide each side by '420'.
0.01904761905 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.01904761905' to each side of the equation.
0.01904761905 + 0.75x + -0.01904761905 + x2 = 0 + -0.01904761905

Reorder the terms:
0.01904761905 + -0.01904761905 + 0.75x + x2 = 0 + -0.01904761905

Combine like terms: 0.01904761905 + -0.01904761905 = 0.00000000000
0.00000000000 + 0.75x + x2 = 0 + -0.01904761905
0.75x + x2 = 0 + -0.01904761905

Combine like terms: 0 + -0.01904761905 = -0.01904761905
0.75x + x2 = -0.01904761905

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 = -0.01904761905 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.01904761905 + 0.140625

Combine like terms: -0.01904761905 + 0.140625 = 0.12157738095
0.140625 + 0.75x + x2 = 0.12157738095

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.12157738095

Calculate the square root of the right side: 0.348679482

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.348679482 and -0.348679482.

Subproblem 1
x + 0.375 = 0.348679482

Simplifying
x + 0.375 = 0.348679482

Reorder the terms:
0.375 + x = 0.348679482

Solving
0.375 + x = 0.348679482

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 = 0.348679482 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.348679482 + -0.375
x = 0.348679482 + -0.375

Combine like terms: 0.348679482 + -0.375 = -0.026320518
x = -0.026320518

Simplifying
x = -0.026320518

Subproblem 2
x + 0.375 = -0.348679482

Simplifying
x + 0.375 = -0.348679482

Reorder the terms:
0.375 + x = -0.348679482

Solving
0.375 + x = -0.348679482

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 = -0.348679482 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.348679482 + -0.375
x = -0.348679482 + -0.375

Combine like terms: -0.348679482 + -0.375 = -0.723679482
x = -0.723679482

Simplifying
x = -0.723679482

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.026320518, -0.723679482}