(0.8x+6)(3x-0.8)=

Solution for (0.8x+6)(3x-0.8)= equation:

Simplifying
(0.8x + 6)(3x + -0.8) = 0

Reorder the terms:
(6 + 0.8x)(3x + -0.8) = 0

Reorder the terms:
(6 + 0.8x)(-0.8 + 3x) = 0

Multiply (6 + 0.8x) * (-0.8 + 3x)
(6(-0.8 + 3x) + 0.8x * (-0.8 + 3x)) = 0
((-0.8 * 6 + 3x * 6) + 0.8x * (-0.8 + 3x)) = 0
((-4.8 + 18x) + 0.8x * (-0.8 + 3x)) = 0
(-4.8 + 18x + (-0.8 * 0.8x + 3x * 0.8x)) = 0
(-4.8 + 18x + (-0.64x + 2.4x2)) = 0

Combine like terms: 18x + -0.64x = 17.36x
(-4.8 + 17.36x + 2.4x2) = 0

Solving
-4.8 + 17.36x + 2.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.4'.
-2 + 7.233333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 7.233333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 7.233333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7.233333333x + x2 = 0 + 2
7.233333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
7.233333333x + x2 = 2

The x term is 7.233333333x.  Take half its coefficient (3.616666667).
Square it (13.08027778) and add it to both sides.

Add '13.08027778' to each side of the equation.
7.233333333x + 13.08027778 + x2 = 2 + 13.08027778

Reorder the terms:
13.08027778 + 7.233333333x + x2 = 2 + 13.08027778

Combine like terms: 2 + 13.08027778 = 15.08027778
13.08027778 + 7.233333333x + x2 = 15.08027778

Factor a perfect square on the left side:
(x + 3.616666667)(x + 3.616666667) = 15.08027778

Calculate the square root of the right side: 3.883333334

Break this problem into two subproblems by setting 
(x + 3.616666667) equal to 3.883333334 and -3.883333334.

Subproblem 1
x + 3.616666667 = 3.883333334

Simplifying
x + 3.616666667 = 3.883333334

Reorder the terms:
3.616666667 + x = 3.883333334

Solving
3.616666667 + x = 3.883333334

Solving for variable 'x'.

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

Add '-3.616666667' to each side of the equation.
3.616666667 + -3.616666667 + x = 3.883333334 + -3.616666667

Combine like terms: 3.616666667 + -3.616666667 = 0.000000000
0.000000000 + x = 3.883333334 + -3.616666667
x = 3.883333334 + -3.616666667

Combine like terms: 3.883333334 + -3.616666667 = 0.266666667
x = 0.266666667

Simplifying
x = 0.266666667

Subproblem 2
x + 3.616666667 = -3.883333334

Simplifying
x + 3.616666667 = -3.883333334

Reorder the terms:
3.616666667 + x = -3.883333334

Solving
3.616666667 + x = -3.883333334

Solving for variable 'x'.

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

Add '-3.616666667' to each side of the equation.
3.616666667 + -3.616666667 + x = -3.883333334 + -3.616666667

Combine like terms: 3.616666667 + -3.616666667 = 0.000000000
0.000000000 + x = -3.883333334 + -3.616666667
x = -3.883333334 + -3.616666667

Combine like terms: -3.883333334 + -3.616666667 = -7.500000001
x = -7.500000001

Simplifying
x = -7.500000001

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.266666667, -7.500000001}