-2(8x+3)=x(x+5)

Solution for -2(8x+3)=x(x+5) equation:

Simplifying
-2(8x + 3) = x(x + 5)

Reorder the terms:
-2(3 + 8x) = x(x + 5)
(3 * -2 + 8x * -2) = x(x + 5)
(-6 + -16x) = x(x + 5)

Reorder the terms:
-6 + -16x = x(5 + x)
-6 + -16x = (5 * x + x * x)
-6 + -16x = (5x + x2)

Solving
-6 + -16x = 5x + x2

Solving for variable 'x'.

Combine like terms: -16x + -5x = -21x
-6 + -21x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
-6 + -21x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-6 + -21x + -1x2 = 0 + x2 + -1x2
-6 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -21x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 21x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 21x + x2 = 0

Solving
6 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 21x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 21x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 21x + x2 = 0 + -6
21x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
21x + x2 = -6

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -6 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -6 + 110.25

Combine like terms: -6 + 110.25 = 104.25
110.25 + 21x + x2 = 104.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + 10.5) equal to 10.210288928 and -10.210288928.

Subproblem 1
x + 10.5 = 10.210288928

Simplifying
x + 10.5 = 10.210288928

Reorder the terms:
10.5 + x = 10.210288928

Solving
10.5 + x = 10.210288928

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 10.210288928 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 10.210288928 + -10.5
x = 10.210288928 + -10.5

Combine like terms: 10.210288928 + -10.5 = -0.289711072
x = -0.289711072

Simplifying
x = -0.289711072

Subproblem 2
x + 10.5 = -10.210288928

Simplifying
x + 10.5 = -10.210288928

Reorder the terms:
10.5 + x = -10.210288928

Solving
10.5 + x = -10.210288928

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -10.210288928 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -10.210288928 + -10.5
x = -10.210288928 + -10.5

Combine like terms: -10.210288928 + -10.5 = -20.710288928
x = -20.710288928

Simplifying
x = -20.710288928

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.289711072, -20.710288928}
Solution
x = {-0.289711072, -20.710288928}