0.5x-0.4x(3x+8)=0.3

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Solution for 0.5x-0.4x(3x+8)=0.3 equation: 


Simplifying
0.5x + -0.4x(3x + 8) = 0.3

Reorder the terms:
0.5x + -0.4x(8 + 3x) = 0.3
0.5x + (8 * -0.4x + 3x * -0.4x) = 0.3
0.5x + (-3.2x + -1.2x2) = 0.3

Combine like terms: 0.5x + -3.2x = -2.7x
-2.7x + -1.2x2 = 0.3

Solving
-2.7x + -1.2x2 = 0.3

Solving for variable 'x'.

Reorder the terms:
-0.3 + -2.7x + -1.2x2 = 0.3 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
-0.3 + -2.7x + -1.2x2 = 0.0

Begin completing the square.  Divide all terms by
-1.2 the coefficient of the squared term: 

Divide each side by '-1.2'.
0.25 + 2.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2.25x + x2 = 0 + -0.25
2.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2.25x + x2 = -0.25

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = -0.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = -0.25 + 1.265625

Combine like terms: -0.25 + 1.265625 = 1.015625
1.265625 + 2.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.007782219 and -1.007782219.


Subproblem 1
x + 1.125 = 1.007782219

Simplifying
x + 1.125 = 1.007782219

Reorder the terms:
1.125 + x = 1.007782219

Solving
1.125 + x = 1.007782219

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.007782219 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.007782219 + -1.125
x = 1.007782219 + -1.125

Combine like terms: 1.007782219 + -1.125 = -0.117217781
x = -0.117217781

Simplifying
x = -0.117217781


Subproblem 2
x + 1.125 = -1.007782219

Simplifying
x + 1.125 = -1.007782219

Reorder the terms:
1.125 + x = -1.007782219

Solving
1.125 + x = -1.007782219

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.007782219 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.007782219 + -1.125
x = -1.007782219 + -1.125

Combine like terms: -1.007782219 + -1.125 = -2.132782219
x = -2.132782219

Simplifying
x = -2.132782219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.117217781, -2.132782219}

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