18x(4+5x)=13

Solution for 18x(4+5x)=13 equation:

Simplifying
18x(4 + 5x) = 13
(4 * 18x + 5x * 18x) = 13
(72x + 90x2) = 13

Solving
72x + 90x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 72x + 90x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 72x + 90x2 = 0

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

Divide each side by '90'.
-0.1444444444 + 0.8x + x2 = 0.0

Move the constant term to the right:

Add '0.1444444444' to each side of the equation.
-0.1444444444 + 0.8x + 0.1444444444 + x2 = 0.0 + 0.1444444444

Reorder the terms:
-0.1444444444 + 0.1444444444 + 0.8x + x2 = 0.0 + 0.1444444444

Combine like terms: -0.1444444444 + 0.1444444444 = 0.0000000000
0.0000000000 + 0.8x + x2 = 0.0 + 0.1444444444
0.8x + x2 = 0.0 + 0.1444444444

Combine like terms: 0.0 + 0.1444444444 = 0.1444444444
0.8x + x2 = 0.1444444444

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.1444444444 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.1444444444 + 0.16

Combine like terms: 0.1444444444 + 0.16 = 0.3044444444
0.16 + 0.8x + x2 = 0.3044444444

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.3044444444

Calculate the square root of the right side: 0.551764845

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.551764845 and -0.551764845.

Subproblem 1
x + 0.4 = 0.551764845

Simplifying
x + 0.4 = 0.551764845

Reorder the terms:
0.4 + x = 0.551764845

Solving
0.4 + x = 0.551764845

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.551764845 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.551764845 + -0.4
x = 0.551764845 + -0.4

Combine like terms: 0.551764845 + -0.4 = 0.151764845
x = 0.151764845

Simplifying
x = 0.151764845

Subproblem 2
x + 0.4 = -0.551764845

Simplifying
x + 0.4 = -0.551764845

Reorder the terms:
0.4 + x = -0.551764845

Solving
0.4 + x = -0.551764845

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.551764845 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.551764845 + -0.4
x = -0.551764845 + -0.4

Combine like terms: -0.551764845 + -0.4 = -0.951764845
x = -0.951764845

Simplifying
x = -0.951764845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.151764845, -0.951764845}