4m^2+48m-4=0

Solution for 4m^2+48m-4=0 equation:

Simplifying
4m2 + 48m + -4 = 0

Reorder the terms:
-4 + 48m + 4m2 = 0

Solving
-4 + 48m + 4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 12m + m2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 12m + m2)' equal to zero and attempt to solve:

Simplifying
-1 + 12m + m2 = 0

Solving
-1 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 12m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + 12m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 12m + m2 = 0 + 1
12m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
12m + m2 = 1

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

Add '36' to each side of the equation.
12m + 36 + m2 = 1 + 36

Reorder the terms:
36 + 12m + m2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + 12m + m2 = 37

Factor a perfect square on the left side:
(m + 6)(m + 6) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(m + 6) equal to 6.08276253 and -6.08276253.

Subproblem 1
m + 6 = 6.08276253

Simplifying
m + 6 = 6.08276253

Reorder the terms:
6 + m = 6.08276253

Solving
6 + m = 6.08276253

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = 6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + m = 6.08276253 + -6
m = 6.08276253 + -6

Combine like terms: 6.08276253 + -6 = 0.08276253
m = 0.08276253

Simplifying
m = 0.08276253

Subproblem 2
m + 6 = -6.08276253

Simplifying
m + 6 = -6.08276253

Reorder the terms:
6 + m = -6.08276253

Solving
6 + m = -6.08276253

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = -6.08276253 + -6

Combine like terms: 6 + -6 = 0
0 + m = -6.08276253 + -6
m = -6.08276253 + -6

Combine like terms: -6.08276253 + -6 = -12.08276253
m = -12.08276253

Simplifying
m = -12.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.08276253, -12.08276253}
Solution
m = {0.08276253, -12.08276253}