m(2m-5)+m=7m(m-6)+16

Solution for m(2m-5)+m=7m(m-6)+16 equation:

Simplifying
m(2m + -5) + m = 7m(m + -6) + 16

Reorder the terms:
m(-5 + 2m) + m = 7m(m + -6) + 16
(-5 * m + 2m * m) + m = 7m(m + -6) + 16
(-5m + 2m2) + m = 7m(m + -6) + 16

Reorder the terms:
-5m + m + 2m2 = 7m(m + -6) + 16

Combine like terms: -5m + m = -4m
-4m + 2m2 = 7m(m + -6) + 16

Reorder the terms:
-4m + 2m2 = 7m(-6 + m) + 16
-4m + 2m2 = (-6 * 7m + m * 7m) + 16
-4m + 2m2 = (-42m + 7m2) + 16

Reorder the terms:
-4m + 2m2 = 16 + -42m + 7m2

Solving
-4m + 2m2 = 16 + -42m + 7m2

Solving for variable 'm'.

Reorder the terms:
-16 + -4m + 42m + 2m2 + -7m2 = 16 + -42m + 7m2 + -16 + 42m + -7m2

Combine like terms: -4m + 42m = 38m
-16 + 38m + 2m2 + -7m2 = 16 + -42m + 7m2 + -16 + 42m + -7m2

Combine like terms: 2m2 + -7m2 = -5m2
-16 + 38m + -5m2 = 16 + -42m + 7m2 + -16 + 42m + -7m2

Reorder the terms:
-16 + 38m + -5m2 = 16 + -16 + -42m + 42m + 7m2 + -7m2

Combine like terms: 16 + -16 = 0
-16 + 38m + -5m2 = 0 + -42m + 42m + 7m2 + -7m2
-16 + 38m + -5m2 = -42m + 42m + 7m2 + -7m2

Combine like terms: -42m + 42m = 0
-16 + 38m + -5m2 = 0 + 7m2 + -7m2
-16 + 38m + -5m2 = 7m2 + -7m2

Combine like terms: 7m2 + -7m2 = 0
-16 + 38m + -5m2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
3.2 + -7.6m + m2 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + -7.6m + -3.2 + m2 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + -7.6m + m2 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + -7.6m + m2 = 0 + -3.2
-7.6m + m2 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
-7.6m + m2 = -3.2

The m term is -7.6m.  Take half its coefficient (-3.8).
Square it (14.44) and add it to both sides.

Add '14.44' to each side of the equation.
-7.6m + 14.44 + m2 = -3.2 + 14.44

Reorder the terms:
14.44 + -7.6m + m2 = -3.2 + 14.44

Combine like terms: -3.2 + 14.44 = 11.24
14.44 + -7.6m + m2 = 11.24

Factor a perfect square on the left side:
(m + -3.8)(m + -3.8) = 11.24

Calculate the square root of the right side: 3.352610923

Break this problem into two subproblems by setting 
(m + -3.8) equal to 3.352610923 and -3.352610923.

Subproblem 1
m + -3.8 = 3.352610923

Simplifying
m + -3.8 = 3.352610923

Reorder the terms:
-3.8 + m = 3.352610923

Solving
-3.8 + m = 3.352610923

Solving for variable 'm'.

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

Add '3.8' to each side of the equation.
-3.8 + 3.8 + m = 3.352610923 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + m = 3.352610923 + 3.8
m = 3.352610923 + 3.8

Combine like terms: 3.352610923 + 3.8 = 7.152610923
m = 7.152610923

Simplifying
m = 7.152610923

Subproblem 2
m + -3.8 = -3.352610923

Simplifying
m + -3.8 = -3.352610923

Reorder the terms:
-3.8 + m = -3.352610923

Solving
-3.8 + m = -3.352610923

Solving for variable 'm'.

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

Add '3.8' to each side of the equation.
-3.8 + 3.8 + m = -3.352610923 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + m = -3.352610923 + 3.8
m = -3.352610923 + 3.8

Combine like terms: -3.352610923 + 3.8 = 0.447389077
m = 0.447389077

Simplifying
m = 0.447389077

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.152610923, 0.447389077}