7-m(m-4)=-3m+2(m+1)

Solution for 7-m(m-4)=-3m+2(m+1) equation:

Simplifying
7 + -1m(m + -4) = -3m + 2(m + 1)

Reorder the terms:
7 + -1m(-4 + m) = -3m + 2(m + 1)
7 + (-4 * -1m + m * -1m) = -3m + 2(m + 1)
7 + (4m + -1m2) = -3m + 2(m + 1)

Reorder the terms:
7 + 4m + -1m2 = -3m + 2(1 + m)
7 + 4m + -1m2 = -3m + (1 * 2 + m * 2)
7 + 4m + -1m2 = -3m + (2 + 2m)

Reorder the terms:
7 + 4m + -1m2 = 2 + -3m + 2m

Combine like terms: -3m + 2m = -1m
7 + 4m + -1m2 = 2 + -1m

Solving
7 + 4m + -1m2 = 2 + -1m

Solving for variable 'm'.

Reorder the terms:
7 + -2 + 4m + m + -1m2 = 2 + -1m + -2 + m

Combine like terms: 7 + -2 = 5
5 + 4m + m + -1m2 = 2 + -1m + -2 + m

Combine like terms: 4m + m = 5m
5 + 5m + -1m2 = 2 + -1m + -2 + m

Reorder the terms:
5 + 5m + -1m2 = 2 + -2 + -1m + m

Combine like terms: 2 + -2 = 0
5 + 5m + -1m2 = 0 + -1m + m
5 + 5m + -1m2 = -1m + m

Combine like terms: -1m + m = 0
5 + 5m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + -5m + m2 = 0

Move the constant term to the right:

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

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

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

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

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 = 5 + 6.25

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

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5m + m2 = 11.25

Factor a perfect square on the left side:
(m + -2.5)(m + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(m + -2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
m + -2.5 = 3.354101966

Simplifying
m + -2.5 = 3.354101966

Reorder the terms:
-2.5 + m = 3.354101966

Solving
-2.5 + m = 3.354101966

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 = 3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = 3.354101966 + 2.5
m = 3.354101966 + 2.5

Combine like terms: 3.354101966 + 2.5 = 5.854101966
m = 5.854101966

Simplifying
m = 5.854101966

Subproblem 2
m + -2.5 = -3.354101966

Simplifying
m + -2.5 = -3.354101966

Reorder the terms:
-2.5 + m = -3.354101966

Solving
-2.5 + m = -3.354101966

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 = -3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + m = -3.354101966 + 2.5
m = -3.354101966 + 2.5

Combine like terms: -3.354101966 + 2.5 = -0.854101966
m = -0.854101966

Simplifying
m = -0.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.854101966, -0.854101966}