(4x+4.3)(9x+2.8)=180

Solution for (4x+4.3)(9x+2.8)=180 equation:

Simplifying
(4x + 4.3)(9x + 2.8) = 180

Reorder the terms:
(4.3 + 4x)(9x + 2.8) = 180

Reorder the terms:
(4.3 + 4x)(2.8 + 9x) = 180

Multiply (4.3 + 4x) * (2.8 + 9x)
(4.3(2.8 + 9x) + 4x * (2.8 + 9x)) = 180
((2.8 * 4.3 + 9x * 4.3) + 4x * (2.8 + 9x)) = 180
((12.04 + 38.7x) + 4x * (2.8 + 9x)) = 180
(12.04 + 38.7x + (2.8 * 4x + 9x * 4x)) = 180
(12.04 + 38.7x + (11.2x + 36x2)) = 180

Combine like terms: 38.7x + 11.2x = 49.9x
(12.04 + 49.9x + 36x2) = 180

Solving
12.04 + 49.9x + 36x2 = 180

Solving for variable 'x'.

Reorder the terms:
12.04 + -180 + 49.9x + 36x2 = 180 + -180

Combine like terms: 12.04 + -180 = -167.96
-167.96 + 49.9x + 36x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-167.96 + 49.9x + 36x2 = 0

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

Divide each side by '36'.
-4.665555556 + 1.386111111x + x2 = 0

Move the constant term to the right:

Add '4.665555556' to each side of the equation.
-4.665555556 + 1.386111111x + 4.665555556 + x2 = 0 + 4.665555556

Reorder the terms:
-4.665555556 + 4.665555556 + 1.386111111x + x2 = 0 + 4.665555556

Combine like terms: -4.665555556 + 4.665555556 = 0.000000000
0.000000000 + 1.386111111x + x2 = 0 + 4.665555556
1.386111111x + x2 = 0 + 4.665555556

Combine like terms: 0 + 4.665555556 = 4.665555556
1.386111111x + x2 = 4.665555556

The x term is 1.386111111x.  Take half its coefficient (0.6930555555).
Square it (0.4803260030) and add it to both sides.

Add '0.4803260030' to each side of the equation.
1.386111111x + 0.4803260030 + x2 = 4.665555556 + 0.4803260030

Reorder the terms:
0.4803260030 + 1.386111111x + x2 = 4.665555556 + 0.4803260030

Combine like terms: 4.665555556 + 0.4803260030 = 5.145881559
0.4803260030 + 1.386111111x + x2 = 5.145881559

Factor a perfect square on the left side:
(x + 0.6930555555)(x + 0.6930555555) = 5.145881559

Calculate the square root of the right side: 2.268453561

Break this problem into two subproblems by setting 
(x + 0.6930555555) equal to 2.268453561 and -2.268453561.

Subproblem 1
x + 0.6930555555 = 2.268453561

Simplifying
x + 0.6930555555 = 2.268453561

Reorder the terms:
0.6930555555 + x = 2.268453561

Solving
0.6930555555 + x = 2.268453561

Solving for variable 'x'.

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

Add '-0.6930555555' to each side of the equation.
0.6930555555 + -0.6930555555 + x = 2.268453561 + -0.6930555555

Combine like terms: 0.6930555555 + -0.6930555555 = 0.0000000000
0.0000000000 + x = 2.268453561 + -0.6930555555
x = 2.268453561 + -0.6930555555

Combine like terms: 2.268453561 + -0.6930555555 = 1.5753980055
x = 1.5753980055

Simplifying
x = 1.5753980055

Subproblem 2
x + 0.6930555555 = -2.268453561

Simplifying
x + 0.6930555555 = -2.268453561

Reorder the terms:
0.6930555555 + x = -2.268453561

Solving
0.6930555555 + x = -2.268453561

Solving for variable 'x'.

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

Add '-0.6930555555' to each side of the equation.
0.6930555555 + -0.6930555555 + x = -2.268453561 + -0.6930555555

Combine like terms: 0.6930555555 + -0.6930555555 = 0.0000000000
0.0000000000 + x = -2.268453561 + -0.6930555555
x = -2.268453561 + -0.6930555555

Combine like terms: -2.268453561 + -0.6930555555 = -2.9615091165
x = -2.9615091165

Simplifying
x = -2.9615091165

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5753980055, -2.9615091165}