x(2x-2)=3360

Solution for x(2x-2)=3360 equation:

Simplifying
x(2x + -2) = 3360

Reorder the terms:
x(-2 + 2x) = 3360
(-2 * x + 2x * x) = 3360
(-2x + 2x2) = 3360

Solving
-2x + 2x2 = 3360

Solving for variable 'x'.

Reorder the terms:
-3360 + -2x + 2x2 = 3360 + -3360

Combine like terms: 3360 + -3360 = 0
-3360 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1680 + -1x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1680 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-1680 + -1x + x2 = 0

Solving
-1680 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1680' to each side of the equation.
-1680 + -1x + 1680 + x2 = 0 + 1680

Reorder the terms:
-1680 + 1680 + -1x + x2 = 0 + 1680

Combine like terms: -1680 + 1680 = 0
0 + -1x + x2 = 0 + 1680
-1x + x2 = 0 + 1680

Combine like terms: 0 + 1680 = 1680
-1x + x2 = 1680

The x term is -1x.  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.
-1x + 0.25 + x2 = 1680 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1680 + 0.25

Combine like terms: 1680 + 0.25 = 1680.25
0.25 + -1x + x2 = 1680.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1680.25

Calculate the square root of the right side: 40.990852638

Break this problem into two subproblems by setting 
(x + -0.5) equal to 40.990852638 and -40.990852638.

Subproblem 1
x + -0.5 = 40.990852638

Simplifying
x + -0.5 = 40.990852638

Reorder the terms:
-0.5 + x = 40.990852638

Solving
-0.5 + x = 40.990852638

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 = 40.990852638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 40.990852638 + 0.5
x = 40.990852638 + 0.5

Combine like terms: 40.990852638 + 0.5 = 41.490852638
x = 41.490852638

Simplifying
x = 41.490852638

Subproblem 2
x + -0.5 = -40.990852638

Simplifying
x + -0.5 = -40.990852638

Reorder the terms:
-0.5 + x = -40.990852638

Solving
-0.5 + x = -40.990852638

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 = -40.990852638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -40.990852638 + 0.5
x = -40.990852638 + 0.5

Combine like terms: -40.990852638 + 0.5 = -40.490852638
x = -40.490852638

Simplifying
x = -40.490852638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.490852638, -40.490852638}
Solution
x = {41.490852638, -40.490852638}