-4(x+2)5x=13

Solution for -4(x+2)5x=13 equation:

Simplifying
-4(x + 2) * 5x = 13

Reorder the terms:
-4(2 + x) * 5x = 13

Reorder the terms for easier multiplication:
-4 * 5x(2 + x) = 13

Multiply -4 * 5
-20x(2 + x) = 13
(2 * -20x + x * -20x) = 13
(-40x + -20x2) = 13

Solving
-40x + -20x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -40x + -20x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -40x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 40x + 20x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + 40x + 20x2)' equal to zero and attempt to solve:

Simplifying
13 + 40x + 20x2 = 0

Solving
13 + 40x + 20x2 = 0

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

Divide each side by '20'.
0.65 + 2x + x2 = 0.0

Move the constant term to the right:

Add '-0.65' to each side of the equation.
0.65 + 2x + -0.65 + x2 = 0.0 + -0.65

Reorder the terms:
0.65 + -0.65 + 2x + x2 = 0.0 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + 2x + x2 = 0.0 + -0.65
2x + x2 = 0.0 + -0.65

Combine like terms: 0.0 + -0.65 = -0.65
2x + x2 = -0.65

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.65 + 1

Reorder the terms:
1 + 2x + x2 = -0.65 + 1

Combine like terms: -0.65 + 1 = 0.35
1 + 2x + x2 = 0.35

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(x + 1) equal to 0.591607978 and -0.591607978.

Subproblem 1
x + 1 = 0.591607978

Simplifying
x + 1 = 0.591607978

Reorder the terms:
1 + x = 0.591607978

Solving
1 + x = 0.591607978

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.591607978 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.591607978 + -1
x = 0.591607978 + -1

Combine like terms: 0.591607978 + -1 = -0.408392022
x = -0.408392022

Simplifying
x = -0.408392022

Subproblem 2
x + 1 = -0.591607978

Simplifying
x + 1 = -0.591607978

Reorder the terms:
1 + x = -0.591607978

Solving
1 + x = -0.591607978

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.591607978 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.591607978 + -1
x = -0.591607978 + -1

Combine like terms: -0.591607978 + -1 = -1.591607978
x = -1.591607978

Simplifying
x = -1.591607978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.408392022, -1.591607978}
Solution
x = {-0.408392022, -1.591607978}