2x(8x^2+8x-9)=0

Solution for 2x(8x^2+8x-9)=0 equation:

Simplifying
2x(8x2 + 8x + -9) = 0

Reorder the terms:
2x(-9 + 8x + 8x2) = 0
(-9 * 2x + 8x * 2x + 8x2 * 2x) = 0
(-18x + 16x2 + 16x3) = 0

Solving
-18x + 16x2 + 16x3 = 0

Solving for variable 'x'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-9 + 8x + 8x2)' equal to zero and attempt to solve:

Simplifying
-9 + 8x + 8x2 = 0

Solving
-9 + 8x + 8x2 = 0

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

Divide each side by '8'.
-1.125 + x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x + x2 = 0 + 1.125
x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
x + x2 = 1.125

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.125 + 0.25

Combine like terms: 1.125 + 0.25 = 1.375
1.25 + x2 = 1.375

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.375

Calculate the square root of the right side: 1.17260394

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.17260394 and -1.17260394.

Subproblem 1
x + 0.5 = 1.17260394

Simplifying
x + 0.5 = 1.17260394

Reorder the terms:
0.5 + x = 1.17260394

Solving
0.5 + x = 1.17260394

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.17260394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.17260394 + -0.5
x = 1.17260394 + -0.5

Combine like terms: 1.17260394 + -0.5 = 0.67260394
x = 0.67260394

Simplifying
x = 0.67260394

Subproblem 2
x + 0.5 = -1.17260394

Simplifying
x + 0.5 = -1.17260394

Reorder the terms:
0.5 + x = -1.17260394

Solving
0.5 + x = -1.17260394

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.17260394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.17260394 + -0.5
x = -1.17260394 + -0.5

Combine like terms: -1.17260394 + -0.5 = -1.67260394
x = -1.67260394

Simplifying
x = -1.67260394

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.67260394, -1.67260394}
Solution
x = {0, 0.67260394, -1.67260394}