(36x+4)*(24x)=31

Solution for (36x+4)*(24x)=31 equation:

Simplifying
(36x + 4)(24x) = 31

Reorder the terms:
(4 + 36x)(24x) = 31

Remove parenthesis around (24x)
(4 + 36x) * 24x = 31

Reorder the terms for easier multiplication:
24x(4 + 36x) = 31
(4 * 24x + 36x * 24x) = 31
(96x + 864x2) = 31

Solving
96x + 864x2 = 31

Solving for variable 'x'.

Reorder the terms:
-31 + 96x + 864x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 96x + 864x2 = 0

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

Divide each side by '864'.
-0.03587962963 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.03587962963' to each side of the equation.
-0.03587962963 + 0.1111111111x + 0.03587962963 + x2 = 0 + 0.03587962963

Reorder the terms:
-0.03587962963 + 0.03587962963 + 0.1111111111x + x2 = 0 + 0.03587962963

Combine like terms: -0.03587962963 + 0.03587962963 = 0.00000000000
0.00000000000 + 0.1111111111x + x2 = 0 + 0.03587962963
0.1111111111x + x2 = 0 + 0.03587962963

Combine like terms: 0 + 0.03587962963 = 0.03587962963
0.1111111111x + x2 = 0.03587962963

The x term is 0.1111111111x.  Take half its coefficient (0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
0.1111111111x + 0.003086419752 + x2 = 0.03587962963 + 0.003086419752

Reorder the terms:
0.003086419752 + 0.1111111111x + x2 = 0.03587962963 + 0.003086419752

Combine like terms: 0.03587962963 + 0.003086419752 = 0.038966049382
0.003086419752 + 0.1111111111x + x2 = 0.038966049382

Factor a perfect square on the left side:
(x + 0.05555555555)(x + 0.05555555555) = 0.038966049382

Calculate the square root of the right side: 0.1973982

Break this problem into two subproblems by setting 
(x + 0.05555555555) equal to 0.1973982 and -0.1973982.

Subproblem 1
x + 0.05555555555 = 0.1973982

Simplifying
x + 0.05555555555 = 0.1973982

Reorder the terms:
0.05555555555 + x = 0.1973982

Solving
0.05555555555 + x = 0.1973982

Solving for variable 'x'.

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

Add '-0.05555555555' to each side of the equation.
0.05555555555 + -0.05555555555 + x = 0.1973982 + -0.05555555555

Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000
0.00000000000 + x = 0.1973982 + -0.05555555555
x = 0.1973982 + -0.05555555555

Combine like terms: 0.1973982 + -0.05555555555 = 0.14184264445
x = 0.14184264445

Simplifying
x = 0.14184264445

Subproblem 2
x + 0.05555555555 = -0.1973982

Simplifying
x + 0.05555555555 = -0.1973982

Reorder the terms:
0.05555555555 + x = -0.1973982

Solving
0.05555555555 + x = -0.1973982

Solving for variable 'x'.

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

Add '-0.05555555555' to each side of the equation.
0.05555555555 + -0.05555555555 + x = -0.1973982 + -0.05555555555

Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000
0.00000000000 + x = -0.1973982 + -0.05555555555
x = -0.1973982 + -0.05555555555

Combine like terms: -0.1973982 + -0.05555555555 = -0.25295375555
x = -0.25295375555

Simplifying
x = -0.25295375555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.14184264445, -0.25295375555}