8x(9x-6)=40x+16

Solution for 8x(9x-6)=40x+16 equation:

Simplifying
8x(9x + -6) = 40x + 16

Reorder the terms:
8x(-6 + 9x) = 40x + 16
(-6 * 8x + 9x * 8x) = 40x + 16
(-48x + 72x2) = 40x + 16

Reorder the terms:
-48x + 72x2 = 16 + 40x

Solving
-48x + 72x2 = 16 + 40x

Solving for variable 'x'.

Reorder the terms:
-16 + -48x + -40x + 72x2 = 16 + 40x + -16 + -40x

Combine like terms: -48x + -40x = -88x
-16 + -88x + 72x2 = 16 + 40x + -16 + -40x

Reorder the terms:
-16 + -88x + 72x2 = 16 + -16 + 40x + -40x

Combine like terms: 16 + -16 = 0
-16 + -88x + 72x2 = 0 + 40x + -40x
-16 + -88x + 72x2 = 40x + -40x

Combine like terms: 40x + -40x = 0
-16 + -88x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -11x + 9x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-2 + -11x + 9x2)' equal to zero and attempt to solve:

Simplifying
-2 + -11x + 9x2 = 0

Solving
-2 + -11x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + -1.222222222x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -1.222222222x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -1.222222222x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -1.222222222x + x2 = 0 + 0.2222222222
-1.222222222x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-1.222222222x + x2 = 0.2222222222

The x term is -1.222222222x.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222x + 0.3734567900 + x2 = 0.2222222222 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222x + x2 = 0.2222222222 + 0.3734567900

Combine like terms: 0.2222222222 + 0.3734567900 = 0.5956790122
0.3734567900 + -1.222222222x + x2 = 0.5956790122

Factor a perfect square on the left side:
(x + -0.611111111)(x + -0.611111111) = 0.5956790122

Calculate the square root of the right side: 0.771802444

Break this problem into two subproblems by setting 
(x + -0.611111111) equal to 0.771802444 and -0.771802444.

Subproblem 1
x + -0.611111111 = 0.771802444

Simplifying
x + -0.611111111 = 0.771802444

Reorder the terms:
-0.611111111 + x = 0.771802444

Solving
-0.611111111 + x = 0.771802444

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = 0.771802444 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = 0.771802444 + 0.611111111
x = 0.771802444 + 0.611111111

Combine like terms: 0.771802444 + 0.611111111 = 1.382913555
x = 1.382913555

Simplifying
x = 1.382913555

Subproblem 2
x + -0.611111111 = -0.771802444

Simplifying
x + -0.611111111 = -0.771802444

Reorder the terms:
-0.611111111 + x = -0.771802444

Solving
-0.611111111 + x = -0.771802444

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = -0.771802444 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = -0.771802444 + 0.611111111
x = -0.771802444 + 0.611111111

Combine like terms: -0.771802444 + 0.611111111 = -0.160691333
x = -0.160691333

Simplifying
x = -0.160691333

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.382913555, -0.160691333}
Solution
x = {1.382913555, -0.160691333}