4x(x-512)=660

Solution for 4x(x-512)=660 equation:

Simplifying
4x(x + -512) = 660

Reorder the terms:
4x(-512 + x) = 660
(-512 * 4x + x * 4x) = 660
(-2048x + 4x2) = 660

Solving
-2048x + 4x2 = 660

Solving for variable 'x'.

Reorder the terms:
-660 + -2048x + 4x2 = 660 + -660

Combine like terms: 660 + -660 = 0
-660 + -2048x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-165 + -512x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-165 + -512x + x2)' equal to zero and attempt to solve:

Simplifying
-165 + -512x + x2 = 0

Solving
-165 + -512x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + -512x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + -512x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + -512x + x2 = 0 + 165
-512x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
-512x + x2 = 165

The x term is -512x.  Take half its coefficient (-256).
Square it (65536) and add it to both sides.

Add '65536' to each side of the equation.
-512x + 65536 + x2 = 165 + 65536

Reorder the terms:
65536 + -512x + x2 = 165 + 65536

Combine like terms: 165 + 65536 = 65701
65536 + -512x + x2 = 65701

Factor a perfect square on the left side:
(x + -256)(x + -256) = 65701

Calculate the square root of the right side: 256.322063038

Break this problem into two subproblems by setting 
(x + -256) equal to 256.322063038 and -256.322063038.

Subproblem 1
x + -256 = 256.322063038

Simplifying
x + -256 = 256.322063038

Reorder the terms:
-256 + x = 256.322063038

Solving
-256 + x = 256.322063038

Solving for variable 'x'.

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

Add '256' to each side of the equation.
-256 + 256 + x = 256.322063038 + 256

Combine like terms: -256 + 256 = 0
0 + x = 256.322063038 + 256
x = 256.322063038 + 256

Combine like terms: 256.322063038 + 256 = 512.322063038
x = 512.322063038

Simplifying
x = 512.322063038

Subproblem 2
x + -256 = -256.322063038

Simplifying
x + -256 = -256.322063038

Reorder the terms:
-256 + x = -256.322063038

Solving
-256 + x = -256.322063038

Solving for variable 'x'.

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

Add '256' to each side of the equation.
-256 + 256 + x = -256.322063038 + 256

Combine like terms: -256 + 256 = 0
0 + x = -256.322063038 + 256
x = -256.322063038 + 256

Combine like terms: -256.322063038 + 256 = -0.322063038
x = -0.322063038

Simplifying
x = -0.322063038

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {512.322063038, -0.322063038}
Solution
x = {512.322063038, -0.322063038}