-9+6m^2=-7m

Solution for -9+6m^2=-7m equation:

Simplifying
-9 + 6m2 = -7m

Solving
-9 + 6m2 = -7m

Solving for variable 'm'.

Reorder the terms:
-9 + 7m + 6m2 = -7m + 7m

Combine like terms: -7m + 7m = 0
-9 + 7m + 6m2 = 0

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

Divide each side by '6'.
-1.5 + 1.166666667m + m2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.166666667m + 1.5 + m2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.166666667m + m2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.166666667m + m2 = 0 + 1.5
1.166666667m + m2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.166666667m + m2 = 1.5

The m term is 1.166666667m.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667m + 0.3402777780 + m2 = 1.5 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667m + m2 = 1.5 + 0.3402777780

Combine like terms: 1.5 + 0.3402777780 = 1.840277778
0.3402777780 + 1.166666667m + m2 = 1.840277778

Factor a perfect square on the left side:
(m + 0.5833333335)(m + 0.5833333335) = 1.840277778

Calculate the square root of the right side: 1.356568383

Break this problem into two subproblems by setting 
(m + 0.5833333335) equal to 1.356568383 and -1.356568383.

Subproblem 1
m + 0.5833333335 = 1.356568383

Simplifying
m + 0.5833333335 = 1.356568383

Reorder the terms:
0.5833333335 + m = 1.356568383

Solving
0.5833333335 + m = 1.356568383

Solving for variable 'm'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + m = 1.356568383 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + m = 1.356568383 + -0.5833333335
m = 1.356568383 + -0.5833333335

Combine like terms: 1.356568383 + -0.5833333335 = 0.7732350495
m = 0.7732350495

Simplifying
m = 0.7732350495

Subproblem 2
m + 0.5833333335 = -1.356568383

Simplifying
m + 0.5833333335 = -1.356568383

Reorder the terms:
0.5833333335 + m = -1.356568383

Solving
0.5833333335 + m = -1.356568383

Solving for variable 'm'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + m = -1.356568383 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + m = -1.356568383 + -0.5833333335
m = -1.356568383 + -0.5833333335

Combine like terms: -1.356568383 + -0.5833333335 = -1.9399017165
m = -1.9399017165

Simplifying
m = -1.9399017165

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.7732350495, -1.9399017165}