(0.3x-0.8)(0.3x+0.2)=

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Solution for (0.3x-0.8)(0.3x+0.2)= equation: 


Simplifying
(0.3x + -0.8)(0.3x + 0.2) = 0

Reorder the terms:
(-0.8 + 0.3x)(0.3x + 0.2) = 0

Reorder the terms:
(-0.8 + 0.3x)(0.2 + 0.3x) = 0

Multiply (-0.8 + 0.3x) * (0.2 + 0.3x)
(-0.8(0.2 + 0.3x) + 0.3x * (0.2 + 0.3x)) = 0
((0.2 * -0.8 + 0.3x * -0.8) + 0.3x * (0.2 + 0.3x)) = 0
((-0.16 + -0.24x) + 0.3x * (0.2 + 0.3x)) = 0
(-0.16 + -0.24x + (0.2 * 0.3x + 0.3x * 0.3x)) = 0
(-0.16 + -0.24x + (0.06x + 0.09x2)) = 0

Combine like terms: -0.24x + 0.06x = -0.18x
(-0.16 + -0.18x + 0.09x2) = 0

Solving
-0.16 + -0.18x + 0.09x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.09'.
-1.777777778 + -2x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -2x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -2x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.777777778
-2x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-2x + x2 = 1.777777778

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.777777778 + 1

Reorder the terms:
1 + -2x + x2 = 1.777777778 + 1

Combine like terms: 1.777777778 + 1 = 2.777777778
1 + -2x + x2 = 2.777777778

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.777777778

Calculate the square root of the right side: 1.666666667

Break this problem into two subproblems by setting 
(x + -1) equal to 1.666666667 and -1.666666667.


Subproblem 1
x + -1 = 1.666666667

Simplifying
x + -1 = 1.666666667

Reorder the terms:
-1 + x = 1.666666667

Solving
-1 + x = 1.666666667

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.666666667 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.666666667 + 1
x = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
x = 2.666666667

Simplifying
x = 2.666666667


Subproblem 2
x + -1 = -1.666666667

Simplifying
x + -1 = -1.666666667

Reorder the terms:
-1 + x = -1.666666667

Solving
-1 + x = -1.666666667

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.666666667 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.666666667 + 1
x = -1.666666667 + 1

Combine like terms: -1.666666667 + 1 = -0.666666667
x = -0.666666667

Simplifying
x = -0.666666667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.666666667, -0.666666667}

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