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 = 7m
7m + 2m2 = 57

Solving
7m + 2m2 = 57

Solving for variable 'm'.

Reorder the terms:
-57 + 7m + 2m2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + 7m + 2m2 = 0

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

Divide each side by '2'.
-28.5 + 3.5m + m2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + 3.5m + 28.5 + m2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + 3.5m + m2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + 3.5m + m2 = 0 + 28.5
3.5m + m2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
3.5m + m2 = 28.5

The m term is 3.5m.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5m + 3.0625 + m2 = 28.5 + 3.0625

Reorder the terms:
3.0625 + 3.5m + m2 = 28.5 + 3.0625

Combine like terms: 28.5 + 3.0625 = 31.5625
3.0625 + 3.5m + m2 = 31.5625

Factor a perfect square on the left side:
(m + 1.75)(m + 1.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(m + 1.75) equal to 5.618051264 and -5.618051264.

Subproblem 1
m + 1.75 = 5.618051264

Simplifying
m + 1.75 = 5.618051264

Reorder the terms:
1.75 + m = 5.618051264

Solving
1.75 + m = 5.618051264

Solving for variable 'm'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + m = 5.618051264 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + m = 5.618051264 + -1.75
m = 5.618051264 + -1.75

Combine like terms: 5.618051264 + -1.75 = 3.868051264
m = 3.868051264

Simplifying
m = 3.868051264

Subproblem 2
m + 1.75 = -5.618051264

Simplifying
m + 1.75 = -5.618051264

Reorder the terms:
1.75 + m = -5.618051264

Solving
1.75 + m = -5.618051264

Solving for variable 'm'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + m = -5.618051264 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + m = -5.618051264 + -1.75
m = -5.618051264 + -1.75

Combine like terms: -5.618051264 + -1.75 = -7.368051264
m = -7.368051264

Simplifying
m = -7.368051264

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.868051264, -7.368051264}