4m^2+7m-6=0

Solution for 4m^2+7m-6=0 equation:

Simplifying
4m2 + 7m + -6 = 0

Reorder the terms:
-6 + 7m + 4m2 = 0

Solving
-6 + 7m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
-1.5 + 1.75m + m2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.75m + 1.5 + m2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.75m + m2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.75m + m2 = 0 + 1.5
1.75m + m2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.75m + m2 = 1.5

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 = 1.5 + 0.765625

Reorder the terms:
0.765625 + 1.75m + m2 = 1.5 + 0.765625

Combine like terms: 1.5 + 0.765625 = 2.265625
0.765625 + 1.75m + m2 = 2.265625

Factor a perfect square on the left side:
(m + 0.875)(m + 0.875) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(m + 0.875) equal to 1.505199322 and -1.505199322.

Subproblem 1
m + 0.875 = 1.505199322

Simplifying
m + 0.875 = 1.505199322

Reorder the terms:
0.875 + m = 1.505199322

Solving
0.875 + m = 1.505199322

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 = 1.505199322 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + m = 1.505199322 + -0.875
m = 1.505199322 + -0.875

Combine like terms: 1.505199322 + -0.875 = 0.630199322
m = 0.630199322

Simplifying
m = 0.630199322

Subproblem 2
m + 0.875 = -1.505199322

Simplifying
m + 0.875 = -1.505199322

Reorder the terms:
0.875 + m = -1.505199322

Solving
0.875 + m = -1.505199322

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 = -1.505199322 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + m = -1.505199322 + -0.875
m = -1.505199322 + -0.875

Combine like terms: -1.505199322 + -0.875 = -2.380199322
m = -2.380199322

Simplifying
m = -2.380199322

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.630199322, -2.380199322}