2m(2m+1)=3m(2m+1)-2

Solution for 2m(2m+1)=3m(2m+1)-2 equation:

Simplifying
2m(2m + 1) = 3m(2m + 1) + -2

Reorder the terms:
2m(1 + 2m) = 3m(2m + 1) + -2
(1 * 2m + 2m * 2m) = 3m(2m + 1) + -2
(2m + 4m2) = 3m(2m + 1) + -2

Reorder the terms:
2m + 4m2 = 3m(1 + 2m) + -2
2m + 4m2 = (1 * 3m + 2m * 3m) + -2
2m + 4m2 = (3m + 6m2) + -2

Reorder the terms:
2m + 4m2 = -2 + 3m + 6m2

Solving
2m + 4m2 = -2 + 3m + 6m2

Solving for variable 'm'.

Reorder the terms:
2 + 2m + -3m + 4m2 + -6m2 = -2 + 3m + 6m2 + 2 + -3m + -6m2

Combine like terms: 2m + -3m = -1m
2 + -1m + 4m2 + -6m2 = -2 + 3m + 6m2 + 2 + -3m + -6m2

Combine like terms: 4m2 + -6m2 = -2m2
2 + -1m + -2m2 = -2 + 3m + 6m2 + 2 + -3m + -6m2

Reorder the terms:
2 + -1m + -2m2 = -2 + 2 + 3m + -3m + 6m2 + -6m2

Combine like terms: -2 + 2 = 0
2 + -1m + -2m2 = 0 + 3m + -3m + 6m2 + -6m2
2 + -1m + -2m2 = 3m + -3m + 6m2 + -6m2

Combine like terms: 3m + -3m = 0
2 + -1m + -2m2 = 0 + 6m2 + -6m2
2 + -1m + -2m2 = 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
2 + -1m + -2m2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1 + 0.5m + m2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5m + m2 = 0 + 1
0.5m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5m + m2 = 1

The m term is 0.5m.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5m + 0.0625 + m2 = 1 + 0.0625

Reorder the terms:
0.0625 + 0.5m + m2 = 1 + 0.0625

Combine like terms: 1 + 0.0625 = 1.0625
0.0625 + 0.5m + m2 = 1.0625

Factor a perfect square on the left side:
(m + 0.25)(m + 0.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(m + 0.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
m + 0.25 = 1.030776406

Simplifying
m + 0.25 = 1.030776406

Reorder the terms:
0.25 + m = 1.030776406

Solving
0.25 + m = 1.030776406

Solving for variable 'm'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + m = 1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + m = 1.030776406 + -0.25
m = 1.030776406 + -0.25

Combine like terms: 1.030776406 + -0.25 = 0.780776406
m = 0.780776406

Simplifying
m = 0.780776406

Subproblem 2
m + 0.25 = -1.030776406

Simplifying
m + 0.25 = -1.030776406

Reorder the terms:
0.25 + m = -1.030776406

Solving
0.25 + m = -1.030776406

Solving for variable 'm'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + m = -1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + m = -1.030776406 + -0.25
m = -1.030776406 + -0.25

Combine like terms: -1.030776406 + -0.25 = -1.280776406
m = -1.280776406

Simplifying
m = -1.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.780776406, -1.280776406}