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

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

Simplifying
m2 + -2m = 3(1 + m)

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

Solving
-2m + m2 = 3 + 3m

Solving for variable 'm'.

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

Combine like terms: -2m + -3m = -5m
-3 + -5m + m2 = 3 + 3m + -3 + -3m

Reorder the terms:
-3 + -5m + m2 = 3 + -3 + 3m + -3m

Combine like terms: 3 + -3 = 0
-3 + -5m + m2 = 0 + 3m + -3m
-3 + -5m + m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
-3 + -5m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + -5m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5m + m2 = 0 + 3
-5m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5m + m2 = 3

The m term is -5m.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5m + 6.25 + m2 = 3 + 6.25

Reorder the terms:
6.25 + -5m + m2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5m + m2 = 9.25

Factor a perfect square on the left side:
(m + -2.5)(m + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(m + -2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
m + -2.5 = 3.041381265

Simplifying
m + -2.5 = 3.041381265

Reorder the terms:
-2.5 + m = 3.041381265

Solving
-2.5 + m = 3.041381265

Solving for variable 'm'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + m = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = 3.041381265 + 2.5
m = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
m = 5.541381265

Simplifying
m = 5.541381265

Subproblem 2
m + -2.5 = -3.041381265

Simplifying
m + -2.5 = -3.041381265

Reorder the terms:
-2.5 + m = -3.041381265

Solving
-2.5 + m = -3.041381265

Solving for variable 'm'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + m = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = -3.041381265 + 2.5
m = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
m = -0.541381265

Simplifying
m = -0.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.541381265, -0.541381265}