-5(4x+4)-x(2x+1)=

Solution for -5(4x+4)-x(2x+1)= equation:

Simplifying
-5(4x + 4) + -1x(2x + 1) = 0

Reorder the terms:
-5(4 + 4x) + -1x(2x + 1) = 0
(4 * -5 + 4x * -5) + -1x(2x + 1) = 0
(-20 + -20x) + -1x(2x + 1) = 0

Reorder the terms:
-20 + -20x + -1x(1 + 2x) = 0
-20 + -20x + (1 * -1x + 2x * -1x) = 0
-20 + -20x + (-1x + -2x2) = 0

Combine like terms: -20x + -1x = -21x
-20 + -21x + -2x2 = 0

Solving
-20 + -21x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 21x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(20 + 21x + 2x2)' equal to zero and attempt to solve:

Simplifying
20 + 21x + 2x2 = 0

Solving
20 + 21x + 2x2 = 0

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

Divide each side by '2'.
10 + 10.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 10.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 10.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 10.5x + x2 = 0 + -10
10.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
10.5x + x2 = -10

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = -10 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = -10 + 27.5625

Combine like terms: -10 + 27.5625 = 17.5625
27.5625 + 10.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + 5.25) equal to 4.190763654 and -4.190763654.

Subproblem 1
x + 5.25 = 4.190763654

Simplifying
x + 5.25 = 4.190763654

Reorder the terms:
5.25 + x = 4.190763654

Solving
5.25 + x = 4.190763654

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 4.190763654 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 4.190763654 + -5.25
x = 4.190763654 + -5.25

Combine like terms: 4.190763654 + -5.25 = -1.059236346
x = -1.059236346

Simplifying
x = -1.059236346

Subproblem 2
x + 5.25 = -4.190763654

Simplifying
x + 5.25 = -4.190763654

Reorder the terms:
5.25 + x = -4.190763654

Solving
5.25 + x = -4.190763654

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -4.190763654 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -4.190763654 + -5.25
x = -4.190763654 + -5.25

Combine like terms: -4.190763654 + -5.25 = -9.440763654
x = -9.440763654

Simplifying
x = -9.440763654

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.059236346, -9.440763654}
Solution
x = {-1.059236346, -9.440763654}