7(3x+6)4(3+5x)=13+x

Solution for 7(3x+6)4(3+5x)=13+x equation:

Simplifying
7(3x + 6) * 4(3 + 5x) = 13 + x

Reorder the terms:
7(6 + 3x) * 4(3 + 5x) = 13 + x

Reorder the terms for easier multiplication:
7 * 4(6 + 3x)(3 + 5x) = 13 + x

Multiply 7 * 4
28(6 + 3x)(3 + 5x) = 13 + x

Multiply (6 + 3x) * (3 + 5x)
28(6(3 + 5x) + 3x * (3 + 5x)) = 13 + x
28((3 * 6 + 5x * 6) + 3x * (3 + 5x)) = 13 + x
28((18 + 30x) + 3x * (3 + 5x)) = 13 + x
28(18 + 30x + (3 * 3x + 5x * 3x)) = 13 + x
28(18 + 30x + (9x + 15x2)) = 13 + x

Combine like terms: 30x + 9x = 39x
28(18 + 39x + 15x2) = 13 + x
(18 * 28 + 39x * 28 + 15x2 * 28) = 13 + x
(504 + 1092x + 420x2) = 13 + x

Solving
504 + 1092x + 420x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
504 + -13 + 1092x + -1x + 420x2 = 13 + x + -13 + -1x

Combine like terms: 504 + -13 = 491
491 + 1092x + -1x + 420x2 = 13 + x + -13 + -1x

Combine like terms: 1092x + -1x = 1091x
491 + 1091x + 420x2 = 13 + x + -13 + -1x

Reorder the terms:
491 + 1091x + 420x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
491 + 1091x + 420x2 = 0 + x + -1x
491 + 1091x + 420x2 = x + -1x

Combine like terms: x + -1x = 0
491 + 1091x + 420x2 = 0

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

Divide each side by '420'.
1.169047619 + 2.597619048x + x2 = 0.0

Move the constant term to the right:

Add '-1.169047619' to each side of the equation.
1.169047619 + 2.597619048x + -1.169047619 + x2 = 0.0 + -1.169047619

Reorder the terms:
1.169047619 + -1.169047619 + 2.597619048x + x2 = 0.0 + -1.169047619

Combine like terms: 1.169047619 + -1.169047619 = 0.000000000
0.000000000 + 2.597619048x + x2 = 0.0 + -1.169047619
2.597619048x + x2 = 0.0 + -1.169047619

Combine like terms: 0.0 + -1.169047619 = -1.169047619
2.597619048x + x2 = -1.169047619

The x term is 2.597619048x.  Take half its coefficient (1.298809524).
Square it (1.686906180) and add it to both sides.

Add '1.686906180' to each side of the equation.
2.597619048x + 1.686906180 + x2 = -1.169047619 + 1.686906180

Reorder the terms:
1.686906180 + 2.597619048x + x2 = -1.169047619 + 1.686906180

Combine like terms: -1.169047619 + 1.686906180 = 0.517858561
1.686906180 + 2.597619048x + x2 = 0.517858561

Factor a perfect square on the left side:
(x + 1.298809524)(x + 1.298809524) = 0.517858561

Calculate the square root of the right side: 0.719623902

Break this problem into two subproblems by setting 
(x + 1.298809524) equal to 0.719623902 and -0.719623902.

Subproblem 1
x + 1.298809524 = 0.719623902

Simplifying
x + 1.298809524 = 0.719623902

Reorder the terms:
1.298809524 + x = 0.719623902

Solving
1.298809524 + x = 0.719623902

Solving for variable 'x'.

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

Add '-1.298809524' to each side of the equation.
1.298809524 + -1.298809524 + x = 0.719623902 + -1.298809524

Combine like terms: 1.298809524 + -1.298809524 = 0.000000000
0.000000000 + x = 0.719623902 + -1.298809524
x = 0.719623902 + -1.298809524

Combine like terms: 0.719623902 + -1.298809524 = -0.579185622
x = -0.579185622

Simplifying
x = -0.579185622

Subproblem 2
x + 1.298809524 = -0.719623902

Simplifying
x + 1.298809524 = -0.719623902

Reorder the terms:
1.298809524 + x = -0.719623902

Solving
1.298809524 + x = -0.719623902

Solving for variable 'x'.

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

Add '-1.298809524' to each side of the equation.
1.298809524 + -1.298809524 + x = -0.719623902 + -1.298809524

Combine like terms: 1.298809524 + -1.298809524 = 0.000000000
0.000000000 + x = -0.719623902 + -1.298809524
x = -0.719623902 + -1.298809524

Combine like terms: -0.719623902 + -1.298809524 = -2.018433426
x = -2.018433426

Simplifying
x = -2.018433426

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.579185622, -2.018433426}