4x*2(2x+1)=162

Solution for 4x*2(2x+1)=162 equation:

Simplifying
4x * 2(2x + 1) = 162

Reorder the terms:
4x * 2(1 + 2x) = 162

Reorder the terms for easier multiplication:
4 * 2x(1 + 2x) = 162

Multiply 4 * 2
8x(1 + 2x) = 162
(1 * 8x + 2x * 8x) = 162
(8x + 16x2) = 162

Solving
8x + 16x2 = 162

Solving for variable 'x'.

Reorder the terms:
-162 + 8x + 16x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + 8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-81 + 4x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-81 + 4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-81 + 4x + 8x2 = 0

Solving
-81 + 4x + 8x2 = 0

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

Divide each side by '8'.
-10.125 + 0.5x + x2 = 0

Move the constant term to the right:

Add '10.125' to each side of the equation.
-10.125 + 0.5x + 10.125 + x2 = 0 + 10.125

Reorder the terms:
-10.125 + 10.125 + 0.5x + x2 = 0 + 10.125

Combine like terms: -10.125 + 10.125 = 0.000
0.000 + 0.5x + x2 = 0 + 10.125
0.5x + x2 = 0 + 10.125

Combine like terms: 0 + 10.125 = 10.125
0.5x + x2 = 10.125

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 = 10.125 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 10.125 + 0.0625

Combine like terms: 10.125 + 0.0625 = 10.1875
0.0625 + 0.5x + x2 = 10.1875

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 10.1875

Calculate the square root of the right side: 3.191786334

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.191786334 and -3.191786334.

Subproblem 1
x + 0.25 = 3.191786334

Simplifying
x + 0.25 = 3.191786334

Reorder the terms:
0.25 + x = 3.191786334

Solving
0.25 + x = 3.191786334

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 = 3.191786334 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 3.191786334 + -0.25
x = 3.191786334 + -0.25

Combine like terms: 3.191786334 + -0.25 = 2.941786334
x = 2.941786334

Simplifying
x = 2.941786334

Subproblem 2
x + 0.25 = -3.191786334

Simplifying
x + 0.25 = -3.191786334

Reorder the terms:
0.25 + x = -3.191786334

Solving
0.25 + x = -3.191786334

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 = -3.191786334 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -3.191786334 + -0.25
x = -3.191786334 + -0.25

Combine like terms: -3.191786334 + -0.25 = -3.441786334
x = -3.441786334

Simplifying
x = -3.441786334

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.941786334, -3.441786334}
Solution
x = {2.941786334, -3.441786334}