(0.9x+8)(3x-0.2)=

Solution for (0.9x+8)(3x-0.2)= equation:

Simplifying
(0.9x + 8)(3x + -0.2) = 0

Reorder the terms:
(8 + 0.9x)(3x + -0.2) = 0

Reorder the terms:
(8 + 0.9x)(-0.2 + 3x) = 0

Multiply (8 + 0.9x) * (-0.2 + 3x)
(8(-0.2 + 3x) + 0.9x * (-0.2 + 3x)) = 0
((-0.2 * 8 + 3x * 8) + 0.9x * (-0.2 + 3x)) = 0
((-1.6 + 24x) + 0.9x * (-0.2 + 3x)) = 0
(-1.6 + 24x + (-0.2 * 0.9x + 3x * 0.9x)) = 0
(-1.6 + 24x + (-0.18x + 2.7x2)) = 0

Combine like terms: 24x + -0.18x = 23.82x
(-1.6 + 23.82x + 2.7x2) = 0

Solving
-1.6 + 23.82x + 2.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.7'.
-0.5925925926 + 8.822222222x + x2 = 0

Move the constant term to the right:

Add '0.5925925926' to each side of the equation.
-0.5925925926 + 8.822222222x + 0.5925925926 + x2 = 0 + 0.5925925926

Reorder the terms:
-0.5925925926 + 0.5925925926 + 8.822222222x + x2 = 0 + 0.5925925926

Combine like terms: -0.5925925926 + 0.5925925926 = 0.0000000000
0.0000000000 + 8.822222222x + x2 = 0 + 0.5925925926
8.822222222x + x2 = 0 + 0.5925925926

Combine like terms: 0 + 0.5925925926 = 0.5925925926
8.822222222x + x2 = 0.5925925926

The x term is 8.822222222x.  Take half its coefficient (4.411111111).
Square it (19.45790123) and add it to both sides.

Add '19.45790123' to each side of the equation.
8.822222222x + 19.45790123 + x2 = 0.5925925926 + 19.45790123

Reorder the terms:
19.45790123 + 8.822222222x + x2 = 0.5925925926 + 19.45790123

Combine like terms: 0.5925925926 + 19.45790123 = 20.0504938226
19.45790123 + 8.822222222x + x2 = 20.0504938226

Factor a perfect square on the left side:
(x + 4.411111111)(x + 4.411111111) = 20.0504938226

Calculate the square root of the right side: 4.477777777

Break this problem into two subproblems by setting 
(x + 4.411111111) equal to 4.477777777 and -4.477777777.

Subproblem 1
x + 4.411111111 = 4.477777777

Simplifying
x + 4.411111111 = 4.477777777

Reorder the terms:
4.411111111 + x = 4.477777777

Solving
4.411111111 + x = 4.477777777

Solving for variable 'x'.

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

Add '-4.411111111' to each side of the equation.
4.411111111 + -4.411111111 + x = 4.477777777 + -4.411111111

Combine like terms: 4.411111111 + -4.411111111 = 0.000000000
0.000000000 + x = 4.477777777 + -4.411111111
x = 4.477777777 + -4.411111111

Combine like terms: 4.477777777 + -4.411111111 = 0.066666666
x = 0.066666666

Simplifying
x = 0.066666666

Subproblem 2
x + 4.411111111 = -4.477777777

Simplifying
x + 4.411111111 = -4.477777777

Reorder the terms:
4.411111111 + x = -4.477777777

Solving
4.411111111 + x = -4.477777777

Solving for variable 'x'.

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

Add '-4.411111111' to each side of the equation.
4.411111111 + -4.411111111 + x = -4.477777777 + -4.411111111

Combine like terms: 4.411111111 + -4.411111111 = 0.000000000
0.000000000 + x = -4.477777777 + -4.411111111
x = -4.477777777 + -4.411111111

Combine like terms: -4.477777777 + -4.411111111 = -8.888888888
x = -8.888888888

Simplifying
x = -8.888888888

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.066666666, -8.888888888}