4m^2+7m+6=4

Solution for 4m^2+7m+6=4 equation:

Simplifying
4m2 + 7m + 6 = 4

Reorder the terms:
6 + 7m + 4m2 = 4

Solving
6 + 7m + 4m2 = 4

Solving for variable 'm'.

Reorder the terms:
6 + -4 + 7m + 4m2 = 4 + -4

Combine like terms: 6 + -4 = 2
2 + 7m + 4m2 = 4 + -4

Combine like terms: 4 + -4 = 0
2 + 7m + 4m2 = 0

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

Divide each side by '4'.
0.5 + 1.75m + m2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.75m + -0.5 + m2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 1.75m + m2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.75m + m2 = 0 + -0.5
1.75m + m2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
1.75m + m2 = -0.5

The m term is 1.75m.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75m + 0.765625 + m2 = -0.5 + 0.765625

Reorder the terms:
0.765625 + 1.75m + m2 = -0.5 + 0.765625

Combine like terms: -0.5 + 0.765625 = 0.265625
0.765625 + 1.75m + m2 = 0.265625

Factor a perfect square on the left side:
(m + 0.875)(m + 0.875) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(m + 0.875) equal to 0.515388203 and -0.515388203.

Subproblem 1
m + 0.875 = 0.515388203

Simplifying
m + 0.875 = 0.515388203

Reorder the terms:
0.875 + m = 0.515388203

Solving
0.875 + m = 0.515388203

Solving for variable 'm'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + m = 0.515388203 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + m = 0.515388203 + -0.875
m = 0.515388203 + -0.875

Combine like terms: 0.515388203 + -0.875 = -0.359611797
m = -0.359611797

Simplifying
m = -0.359611797

Subproblem 2
m + 0.875 = -0.515388203

Simplifying
m + 0.875 = -0.515388203

Reorder the terms:
0.875 + m = -0.515388203

Solving
0.875 + m = -0.515388203

Solving for variable 'm'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + m = -0.515388203 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + m = -0.515388203 + -0.875
m = -0.515388203 + -0.875

Combine like terms: -0.515388203 + -0.875 = -1.390388203
m = -1.390388203

Simplifying
m = -1.390388203

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.359611797, -1.390388203}