2x(5+13x)=20

Solution for 2x(5+13x)=20 equation:

Simplifying
2x(5 + 13x) = 20
(5 * 2x + 13x * 2x) = 20
(10x + 26x2) = 20

Solving
10x + 26x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 10x + 26x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 10x + 26x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 5x + 13x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + 5x + 13x2)' equal to zero and attempt to solve:

Simplifying
-10 + 5x + 13x2 = 0

Solving
-10 + 5x + 13x2 = 0

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

Divide each side by '13'.
-0.7692307692 + 0.3846153846x + x2 = 0

Move the constant term to the right:

Add '0.7692307692' to each side of the equation.
-0.7692307692 + 0.3846153846x + 0.7692307692 + x2 = 0 + 0.7692307692

Reorder the terms:
-0.7692307692 + 0.7692307692 + 0.3846153846x + x2 = 0 + 0.7692307692

Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000
0.0000000000 + 0.3846153846x + x2 = 0 + 0.7692307692
0.3846153846x + x2 = 0 + 0.7692307692

Combine like terms: 0 + 0.7692307692 = 0.7692307692
0.3846153846x + x2 = 0.7692307692

The x term is 0.3846153846x.  Take half its coefficient (0.1923076923).
Square it (0.03698224852) and add it to both sides.

Add '0.03698224852' to each side of the equation.
0.3846153846x + 0.03698224852 + x2 = 0.7692307692 + 0.03698224852

Reorder the terms:
0.03698224852 + 0.3846153846x + x2 = 0.7692307692 + 0.03698224852

Combine like terms: 0.7692307692 + 0.03698224852 = 0.80621301772
0.03698224852 + 0.3846153846x + x2 = 0.80621301772

Factor a perfect square on the left side:
(x + 0.1923076923)(x + 0.1923076923) = 0.80621301772

Calculate the square root of the right side: 0.897893656

Break this problem into two subproblems by setting 
(x + 0.1923076923) equal to 0.897893656 and -0.897893656.

Subproblem 1
x + 0.1923076923 = 0.897893656

Simplifying
x + 0.1923076923 = 0.897893656

Reorder the terms:
0.1923076923 + x = 0.897893656

Solving
0.1923076923 + x = 0.897893656

Solving for variable 'x'.

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

Add '-0.1923076923' to each side of the equation.
0.1923076923 + -0.1923076923 + x = 0.897893656 + -0.1923076923

Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000
0.0000000000 + x = 0.897893656 + -0.1923076923
x = 0.897893656 + -0.1923076923

Combine like terms: 0.897893656 + -0.1923076923 = 0.7055859637
x = 0.7055859637

Simplifying
x = 0.7055859637

Subproblem 2
x + 0.1923076923 = -0.897893656

Simplifying
x + 0.1923076923 = -0.897893656

Reorder the terms:
0.1923076923 + x = -0.897893656

Solving
0.1923076923 + x = -0.897893656

Solving for variable 'x'.

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

Add '-0.1923076923' to each side of the equation.
0.1923076923 + -0.1923076923 + x = -0.897893656 + -0.1923076923

Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000
0.0000000000 + x = -0.897893656 + -0.1923076923
x = -0.897893656 + -0.1923076923

Combine like terms: -0.897893656 + -0.1923076923 = -1.0902013483
x = -1.0902013483

Simplifying
x = -1.0902013483

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7055859637, -1.0902013483}
Solution
x = {0.7055859637, -1.0902013483}