20m^2+40m+4=0

Solution for 20m^2+40m+4=0 equation:

Simplifying
20m2 + 40m + 4 = 0

Reorder the terms:
4 + 40m + 20m2 = 0

Solving
4 + 40m + 20m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 10m + 5m2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 10m + 5m2)' equal to zero and attempt to solve:

Simplifying
1 + 10m + 5m2 = 0

Solving
1 + 10m + 5m2 = 0

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

Divide each side by '5'.
0.2 + 2m + m2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2m + -0.2 + m2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2m + m2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2m + m2 = 0 + -0.2
2m + m2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2m + m2 = -0.2

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = -0.2 + 1

Reorder the terms:
1 + 2m + m2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2m + m2 = 0.8

Factor a perfect square on the left side:
(m + 1)(m + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(m + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1
m + 1 = 0.894427191

Simplifying
m + 1 = 0.894427191

Reorder the terms:
1 + m = 0.894427191

Solving
1 + m = 0.894427191

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0.894427191 + -1
m = 0.894427191 + -1

Combine like terms: 0.894427191 + -1 = -0.105572809
m = -0.105572809

Simplifying
m = -0.105572809

Subproblem 2
m + 1 = -0.894427191

Simplifying
m + 1 = -0.894427191

Reorder the terms:
1 + m = -0.894427191

Solving
1 + m = -0.894427191

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + m = -0.894427191 + -1
m = -0.894427191 + -1

Combine like terms: -0.894427191 + -1 = -1.894427191
m = -1.894427191

Simplifying
m = -1.894427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.105572809, -1.894427191}
Solution
m = {-0.105572809, -1.894427191}