4+13x(2-3x)=39x-2(13+2)

Solution for 4+13x(2-3x)=39x-2(13+2) equation:

Simplifying
4 + 13x(2 + -3x) = 39x + -2(13 + 2)
4 + (2 * 13x + -3x * 13x) = 39x + -2(13 + 2)
4 + (26x + -39x2) = 39x + -2(13 + 2)

Combine like terms: 13 + 2 = 15
4 + 26x + -39x2 = 39x + -2(15)

Multiply -2 * 15
4 + 26x + -39x2 = 39x + -30

Reorder the terms:
4 + 26x + -39x2 = -30 + 39x

Solving
4 + 26x + -39x2 = -30 + 39x

Solving for variable 'x'.

Reorder the terms:
4 + 30 + 26x + -39x + -39x2 = -30 + 39x + 30 + -39x

Combine like terms: 4 + 30 = 34
34 + 26x + -39x + -39x2 = -30 + 39x + 30 + -39x

Combine like terms: 26x + -39x = -13x
34 + -13x + -39x2 = -30 + 39x + 30 + -39x

Reorder the terms:
34 + -13x + -39x2 = -30 + 30 + 39x + -39x

Combine like terms: -30 + 30 = 0
34 + -13x + -39x2 = 0 + 39x + -39x
34 + -13x + -39x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
34 + -13x + -39x2 = 0

Begin completing the square.  Divide all terms by
-39 the coefficient of the squared term: 

Divide each side by '-39'.
-0.8717948718 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.8717948718' to each side of the equation.
-0.8717948718 + 0.3333333333x + 0.8717948718 + x2 = 0 + 0.8717948718

Reorder the terms:
-0.8717948718 + 0.8717948718 + 0.3333333333x + x2 = 0 + 0.8717948718

Combine like terms: -0.8717948718 + 0.8717948718 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.8717948718
0.3333333333x + x2 = 0 + 0.8717948718

Combine like terms: 0 + 0.8717948718 = 0.8717948718
0.3333333333x + x2 = 0.8717948718

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.8717948718 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.8717948718 + 0.02777777779

Combine like terms: 0.8717948718 + 0.02777777779 = 0.89957264959
0.02777777779 + 0.3333333333x + x2 = 0.89957264959

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.89957264959

Calculate the square root of the right side: 0.948458038

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.948458038 and -0.948458038.

Subproblem 1
x + 0.1666666667 = 0.948458038

Simplifying
x + 0.1666666667 = 0.948458038

Reorder the terms:
0.1666666667 + x = 0.948458038

Solving
0.1666666667 + x = 0.948458038

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.948458038 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.948458038 + -0.1666666667
x = 0.948458038 + -0.1666666667

Combine like terms: 0.948458038 + -0.1666666667 = 0.7817913713
x = 0.7817913713

Simplifying
x = 0.7817913713

Subproblem 2
x + 0.1666666667 = -0.948458038

Simplifying
x + 0.1666666667 = -0.948458038

Reorder the terms:
0.1666666667 + x = -0.948458038

Solving
0.1666666667 + x = -0.948458038

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.948458038 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.948458038 + -0.1666666667
x = -0.948458038 + -0.1666666667

Combine like terms: -0.948458038 + -0.1666666667 = -1.1151247047
x = -1.1151247047

Simplifying
x = -1.1151247047

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7817913713, -1.1151247047}