4x(2x-2)=10

Solution for 4x(2x-2)=10 equation:

Simplifying
4x(2x + -2) = 10

Reorder the terms:
4x(-2 + 2x) = 10
(-2 * 4x + 2x * 4x) = 10
(-8x + 8x2) = 10

Solving
-8x + 8x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -8x + 8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -4x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -4x + 4x2 = 0

Solving
-5 + -4x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -1x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1x + x2 = 0 + 1.25
-1x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1x + x2 = 1.25

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 = 1.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
0.25 + -1x + x2 = 1.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + -0.5 = 1.224744871

Simplifying
x + -0.5 = 1.224744871

Reorder the terms:
-0.5 + x = 1.224744871

Solving
-0.5 + x = 1.224744871

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 = 1.224744871 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.224744871 + 0.5
x = 1.224744871 + 0.5

Combine like terms: 1.224744871 + 0.5 = 1.724744871
x = 1.724744871

Simplifying
x = 1.724744871

Subproblem 2
x + -0.5 = -1.224744871

Simplifying
x + -0.5 = -1.224744871

Reorder the terms:
-0.5 + x = -1.224744871

Solving
-0.5 + x = -1.224744871

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 = -1.224744871 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.224744871 + 0.5
x = -1.224744871 + 0.5

Combine like terms: -1.224744871 + 0.5 = -0.724744871
x = -0.724744871

Simplifying
x = -0.724744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.724744871, -0.724744871}
Solution
x = {1.724744871, -0.724744871}