3x(9-4x)=8x-1

Solution for 3x(9-4x)=8x-1 equation:

Simplifying
3x(9 + -4x) = 8x + -1
(9 * 3x + -4x * 3x) = 8x + -1
(27x + -12x2) = 8x + -1

Reorder the terms:
27x + -12x2 = -1 + 8x

Solving
27x + -12x2 = -1 + 8x

Solving for variable 'x'.

Reorder the terms:
1 + 27x + -8x + -12x2 = -1 + 8x + 1 + -8x

Combine like terms: 27x + -8x = 19x
1 + 19x + -12x2 = -1 + 8x + 1 + -8x

Reorder the terms:
1 + 19x + -12x2 = -1 + 1 + 8x + -8x

Combine like terms: -1 + 1 = 0
1 + 19x + -12x2 = 0 + 8x + -8x
1 + 19x + -12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
1 + 19x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.08333333333 + -1.583333333x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -1.583333333x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -1.583333333x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -1.583333333x + x2 = 0 + 0.08333333333
-1.583333333x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-1.583333333x + x2 = 0.08333333333

The x term is -1.583333333x.  Take half its coefficient (-0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
-1.583333333x + 0.6267361108 + x2 = 0.08333333333 + 0.6267361108

Reorder the terms:
0.6267361108 + -1.583333333x + x2 = 0.08333333333 + 0.6267361108

Combine like terms: 0.08333333333 + 0.6267361108 = 0.71006944413
0.6267361108 + -1.583333333x + x2 = 0.71006944413

Factor a perfect square on the left side:
(x + -0.7916666665)(x + -0.7916666665) = 0.71006944413

Calculate the square root of the right side: 0.842656184

Break this problem into two subproblems by setting 
(x + -0.7916666665) equal to 0.842656184 and -0.842656184.

Subproblem 1
x + -0.7916666665 = 0.842656184

Simplifying
x + -0.7916666665 = 0.842656184

Reorder the terms:
-0.7916666665 + x = 0.842656184

Solving
-0.7916666665 + x = 0.842656184

Solving for variable 'x'.

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

Add '0.7916666665' to each side of the equation.
-0.7916666665 + 0.7916666665 + x = 0.842656184 + 0.7916666665

Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000
0.0000000000 + x = 0.842656184 + 0.7916666665
x = 0.842656184 + 0.7916666665

Combine like terms: 0.842656184 + 0.7916666665 = 1.6343228505
x = 1.6343228505

Simplifying
x = 1.6343228505

Subproblem 2
x + -0.7916666665 = -0.842656184

Simplifying
x + -0.7916666665 = -0.842656184

Reorder the terms:
-0.7916666665 + x = -0.842656184

Solving
-0.7916666665 + x = -0.842656184

Solving for variable 'x'.

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

Add '0.7916666665' to each side of the equation.
-0.7916666665 + 0.7916666665 + x = -0.842656184 + 0.7916666665

Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000
0.0000000000 + x = -0.842656184 + 0.7916666665
x = -0.842656184 + 0.7916666665

Combine like terms: -0.842656184 + 0.7916666665 = -0.0509895175
x = -0.0509895175

Simplifying
x = -0.0509895175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6343228505, -0.0509895175}