4x^2+48x+20=0

Solution for 4x^2+48x+20=0 equation:

Simplifying
4x2 + 48x + 20 = 0

Reorder the terms:
20 + 48x + 4x2 = 0

Solving
20 + 48x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 12x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 12x + x2 = 0

Solving
5 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 12x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 12x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 12x + x2 = 0 + -5
12x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
12x + x2 = -5

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -5 + 36

Reorder the terms:
36 + 12x + x2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + 12x + x2 = 31

Factor a perfect square on the left side:
(x + 6)(x + 6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 6) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + 6 = 5.567764363

Simplifying
x + 6 = 5.567764363

Reorder the terms:
6 + x = 5.567764363

Solving
6 + x = 5.567764363

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.567764363 + -6
x = 5.567764363 + -6

Combine like terms: 5.567764363 + -6 = -0.432235637
x = -0.432235637

Simplifying
x = -0.432235637

Subproblem 2
x + 6 = -5.567764363

Simplifying
x + 6 = -5.567764363

Reorder the terms:
6 + x = -5.567764363

Solving
6 + x = -5.567764363

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.567764363 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.567764363 + -6
x = -5.567764363 + -6

Combine like terms: -5.567764363 + -6 = -11.567764363
x = -11.567764363

Simplifying
x = -11.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.432235637, -11.567764363}
Solution
x = {-0.432235637, -11.567764363}