1m+(1m-3)2m=57

Solution for 1m+(1m-3)2m=57 equation:

Simplifying
1m + (1m + -3) * 2m = 57

Reorder the terms:
1m + (-3 + 1m) * 2m = 57

Reorder the terms for easier multiplication:
1m + 2m(-3 + 1m) = 57
1m + (-3 * 2m + 1m * 2m) = 57
1m + (-6m + 2m2) = 57

Combine like terms: 1m + -6m = -5m
-5m + 2m2 = 57

Solving
-5m + 2m2 = 57

Solving for variable 'm'.

Reorder the terms:
-57 + -5m + 2m2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + -5m + 2m2 = 0

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

Divide each side by '2'.
-28.5 + -2.5m + m2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + -2.5m + 28.5 + m2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + -2.5m + m2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + -2.5m + m2 = 0 + 28.5
-2.5m + m2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
-2.5m + m2 = 28.5

The m term is -2.5m.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5m + 1.5625 + m2 = 28.5 + 1.5625

Reorder the terms:
1.5625 + -2.5m + m2 = 28.5 + 1.5625

Combine like terms: 28.5 + 1.5625 = 30.0625
1.5625 + -2.5m + m2 = 30.0625

Factor a perfect square on the left side:
(m + -1.25)(m + -1.25) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(m + -1.25) equal to 5.48292805 and -5.48292805.

Subproblem 1
m + -1.25 = 5.48292805

Simplifying
m + -1.25 = 5.48292805

Reorder the terms:
-1.25 + m = 5.48292805

Solving
-1.25 + m = 5.48292805

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = 5.48292805 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = 5.48292805 + 1.25
m = 5.48292805 + 1.25

Combine like terms: 5.48292805 + 1.25 = 6.73292805
m = 6.73292805

Simplifying
m = 6.73292805

Subproblem 2
m + -1.25 = -5.48292805

Simplifying
m + -1.25 = -5.48292805

Reorder the terms:
-1.25 + m = -5.48292805

Solving
-1.25 + m = -5.48292805

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = -5.48292805 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = -5.48292805 + 1.25
m = -5.48292805 + 1.25

Combine like terms: -5.48292805 + 1.25 = -4.23292805
m = -4.23292805

Simplifying
m = -4.23292805

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.73292805, -4.23292805}