2x(x-2)=60

Solution for 2x(x-2)=60 equation:

Simplifying
2x(x + -2) = 60

Reorder the terms:
2x(-2 + x) = 60
(-2 * 2x + x * 2x) = 60
(-4x + 2x2) = 60

Solving
-4x + 2x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -4x + 2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + -2x + x2 = 0

Solving
-30 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -2x + x2 = 0 + 30
-2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-2x + x2 = 30

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 30 + 1

Reorder the terms:
1 + -2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + -2x + x2 = 31

Factor a perfect square on the left side:
(x + -1)(x + -1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -1) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + -1 = 5.567764363

Simplifying
x + -1 = 5.567764363

Reorder the terms:
-1 + x = 5.567764363

Solving
-1 + x = 5.567764363

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.567764363 + 1
x = 5.567764363 + 1

Combine like terms: 5.567764363 + 1 = 6.567764363
x = 6.567764363

Simplifying
x = 6.567764363

Subproblem 2
x + -1 = -5.567764363

Simplifying
x + -1 = -5.567764363

Reorder the terms:
-1 + x = -5.567764363

Solving
-1 + x = -5.567764363

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -5.567764363 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.567764363 + 1
x = -5.567764363 + 1

Combine like terms: -5.567764363 + 1 = -4.567764363
x = -4.567764363

Simplifying
x = -4.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.567764363, -4.567764363}
Solution
x = {6.567764363, -4.567764363}