(18x+5)(-1+8x)+46=180

Solution for (18x+5)(-1+8x)+46=180 equation:

Simplifying
(18x + 5)(-1 + 8x) + 46 = 180

Reorder the terms:
(5 + 18x)(-1 + 8x) + 46 = 180

Multiply (5 + 18x) * (-1 + 8x)
(5(-1 + 8x) + 18x * (-1 + 8x)) + 46 = 180
((-1 * 5 + 8x * 5) + 18x * (-1 + 8x)) + 46 = 180
((-5 + 40x) + 18x * (-1 + 8x)) + 46 = 180
(-5 + 40x + (-1 * 18x + 8x * 18x)) + 46 = 180
(-5 + 40x + (-18x + 144x2)) + 46 = 180

Combine like terms: 40x + -18x = 22x
(-5 + 22x + 144x2) + 46 = 180

Reorder the terms:
-5 + 46 + 22x + 144x2 = 180

Combine like terms: -5 + 46 = 41
41 + 22x + 144x2 = 180

Solving
41 + 22x + 144x2 = 180

Solving for variable 'x'.

Reorder the terms:
41 + -180 + 22x + 144x2 = 180 + -180

Combine like terms: 41 + -180 = -139
-139 + 22x + 144x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-139 + 22x + 144x2 = 0

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

Divide each side by '144'.
-0.9652777778 + 0.1527777778x + x2 = 0

Move the constant term to the right:

Add '0.9652777778' to each side of the equation.
-0.9652777778 + 0.1527777778x + 0.9652777778 + x2 = 0 + 0.9652777778

Reorder the terms:
-0.9652777778 + 0.9652777778 + 0.1527777778x + x2 = 0 + 0.9652777778

Combine like terms: -0.9652777778 + 0.9652777778 = 0.0000000000
0.0000000000 + 0.1527777778x + x2 = 0 + 0.9652777778
0.1527777778x + x2 = 0 + 0.9652777778

Combine like terms: 0 + 0.9652777778 = 0.9652777778
0.1527777778x + x2 = 0.9652777778

The x term is 0.1527777778x.  Take half its coefficient (0.0763888889).
Square it (0.005835262347) and add it to both sides.

Add '0.005835262347' to each side of the equation.
0.1527777778x + 0.005835262347 + x2 = 0.9652777778 + 0.005835262347

Reorder the terms:
0.005835262347 + 0.1527777778x + x2 = 0.9652777778 + 0.005835262347

Combine like terms: 0.9652777778 + 0.005835262347 = 0.971113040147
0.005835262347 + 0.1527777778x + x2 = 0.971113040147

Factor a perfect square on the left side:
(x + 0.0763888889)(x + 0.0763888889) = 0.971113040147

Calculate the square root of the right side: 0.985450679

Break this problem into two subproblems by setting 
(x + 0.0763888889) equal to 0.985450679 and -0.985450679.

Subproblem 1
x + 0.0763888889 = 0.985450679

Simplifying
x + 0.0763888889 = 0.985450679

Reorder the terms:
0.0763888889 + x = 0.985450679

Solving
0.0763888889 + x = 0.985450679

Solving for variable 'x'.

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

Add '-0.0763888889' to each side of the equation.
0.0763888889 + -0.0763888889 + x = 0.985450679 + -0.0763888889

Combine like terms: 0.0763888889 + -0.0763888889 = 0.0000000000
0.0000000000 + x = 0.985450679 + -0.0763888889
x = 0.985450679 + -0.0763888889

Combine like terms: 0.985450679 + -0.0763888889 = 0.9090617901
x = 0.9090617901

Simplifying
x = 0.9090617901

Subproblem 2
x + 0.0763888889 = -0.985450679

Simplifying
x + 0.0763888889 = -0.985450679

Reorder the terms:
0.0763888889 + x = -0.985450679

Solving
0.0763888889 + x = -0.985450679

Solving for variable 'x'.

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

Add '-0.0763888889' to each side of the equation.
0.0763888889 + -0.0763888889 + x = -0.985450679 + -0.0763888889

Combine like terms: 0.0763888889 + -0.0763888889 = 0.0000000000
0.0000000000 + x = -0.985450679 + -0.0763888889
x = -0.985450679 + -0.0763888889

Combine like terms: -0.985450679 + -0.0763888889 = -1.0618395679
x = -1.0618395679

Simplifying
x = -1.0618395679

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9090617901, -1.0618395679}