8=-3(2x+2)7x

Solution for 8=-3(2x+2)7x equation:

Simplifying
8 = -3(2x + 2) * 7x

Reorder the terms:
8 = -3(2 + 2x) * 7x

Reorder the terms for easier multiplication:
8 = -3 * 7x(2 + 2x)

Multiply -3 * 7
8 = -21x(2 + 2x)
8 = (2 * -21x + 2x * -21x)
8 = (-42x + -42x2)

Solving
8 = -42x + -42x2

Solving for variable 'x'.

Reorder the terms:
8 + 42x + 42x2 = -42x + 42x + -42x2 + 42x2

Combine like terms: -42x + 42x = 0
8 + 42x + 42x2 = 0 + -42x2 + 42x2
8 + 42x + 42x2 = -42x2 + 42x2

Combine like terms: -42x2 + 42x2 = 0
8 + 42x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 21x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 21x + 21x2)' equal to zero and attempt to solve:

Simplifying
4 + 21x + 21x2 = 0

Solving
4 + 21x + 21x2 = 0

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

Divide each side by '21'.
0.1904761905 + x + x2 = 0

Move the constant term to the right:

Add '-0.1904761905' to each side of the equation.
0.1904761905 + x + -0.1904761905 + x2 = 0 + -0.1904761905

Reorder the terms:
0.1904761905 + -0.1904761905 + x + x2 = 0 + -0.1904761905

Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000
0.0000000000 + x + x2 = 0 + -0.1904761905
x + x2 = 0 + -0.1904761905

Combine like terms: 0 + -0.1904761905 = -0.1904761905
x + x2 = -0.1904761905

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -0.1904761905 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.1904761905 + 0.25

Combine like terms: -0.1904761905 + 0.25 = 0.0595238095
1.25 + x2 = 0.0595238095

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.0595238095

Calculate the square root of the right side: 0.243975018

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.243975018 and -0.243975018.

Subproblem 1
x + 0.5 = 0.243975018

Simplifying
x + 0.5 = 0.243975018

Reorder the terms:
0.5 + x = 0.243975018

Solving
0.5 + x = 0.243975018

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.243975018 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.243975018 + -0.5
x = 0.243975018 + -0.5

Combine like terms: 0.243975018 + -0.5 = -0.256024982
x = -0.256024982

Simplifying
x = -0.256024982

Subproblem 2
x + 0.5 = -0.243975018

Simplifying
x + 0.5 = -0.243975018

Reorder the terms:
0.5 + x = -0.243975018

Solving
0.5 + x = -0.243975018

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.243975018 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.243975018 + -0.5
x = -0.243975018 + -0.5

Combine like terms: -0.243975018 + -0.5 = -0.743975018
x = -0.743975018

Simplifying
x = -0.743975018

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.256024982, -0.743975018}
Solution
x = {-0.256024982, -0.743975018}