4x(4x+2)=90

Solution for 4x(4x+2)=90 equation:

Simplifying
4x(4x + 2) = 90

Reorder the terms:
4x(2 + 4x) = 90
(2 * 4x + 4x * 4x) = 90
(8x + 16x2) = 90

Solving
8x + 16x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 8x + 16x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 4x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + 4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-45 + 4x + 8x2 = 0

Solving
-45 + 4x + 8x2 = 0

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

Divide each side by '8'.
-5.625 + 0.5x + x2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + 0.5x + 5.625 + x2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + 0.5x + x2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + 0.5x + x2 = 0 + 5.625
0.5x + x2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
0.5x + x2 = 5.625

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 = 5.625 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 5.625 + 0.0625

Combine like terms: 5.625 + 0.0625 = 5.6875
0.0625 + 0.5x + x2 = 5.6875

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 5.6875

Calculate the square root of the right side: 2.384848004

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.384848004 and -2.384848004.

Subproblem 1
x + 0.25 = 2.384848004

Simplifying
x + 0.25 = 2.384848004

Reorder the terms:
0.25 + x = 2.384848004

Solving
0.25 + x = 2.384848004

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 = 2.384848004 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.384848004 + -0.25
x = 2.384848004 + -0.25

Combine like terms: 2.384848004 + -0.25 = 2.134848004
x = 2.134848004

Simplifying
x = 2.134848004

Subproblem 2
x + 0.25 = -2.384848004

Simplifying
x + 0.25 = -2.384848004

Reorder the terms:
0.25 + x = -2.384848004

Solving
0.25 + x = -2.384848004

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 = -2.384848004 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.384848004 + -0.25
x = -2.384848004 + -0.25

Combine like terms: -2.384848004 + -0.25 = -2.634848004
x = -2.634848004

Simplifying
x = -2.634848004

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.134848004, -2.634848004}
Solution
x = {2.134848004, -2.634848004}