2x(4x+2)=10

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

Simplifying
2x(4x + 2) = 10

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

Solving
4x + 8x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 4x + 8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 4x + 8x2 = 0

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

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

Simplifying
-5 + 2x + 4x2 = 0

Solving
-5 + 2x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.5x + x2 = 0 + 1.25
0.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.5x + x2 = 1.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + 0.5x + x2 = 1.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
x + 0.25 = 1.145643924

Simplifying
x + 0.25 = 1.145643924

Reorder the terms:
0.25 + x = 1.145643924

Solving
0.25 + x = 1.145643924

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.145643924 + -0.25
x = 1.145643924 + -0.25

Combine like terms: 1.145643924 + -0.25 = 0.895643924
x = 0.895643924

Simplifying
x = 0.895643924

Subproblem 2
x + 0.25 = -1.145643924

Simplifying
x + 0.25 = -1.145643924

Reorder the terms:
0.25 + x = -1.145643924

Solving
0.25 + x = -1.145643924

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.145643924 + -0.25
x = -1.145643924 + -0.25

Combine like terms: -1.145643924 + -0.25 = -1.395643924
x = -1.395643924

Simplifying
x = -1.395643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.895643924, -1.395643924}
Solution
x = {0.895643924, -1.395643924}