-6m+16-6m(m-1)=4m-(2m-1)-8m+9

Solution for -6m+16-6m(m-1)=4m-(2m-1)-8m+9 equation:

Simplifying
-6m + 16 + -6m(m + -1) = 4m + -1(2m + -1) + -8m + 9

Reorder the terms:
-6m + 16 + -6m(-1 + m) = 4m + -1(2m + -1) + -8m + 9
-6m + 16 + (-1 * -6m + m * -6m) = 4m + -1(2m + -1) + -8m + 9
-6m + 16 + (6m + -6m2) = 4m + -1(2m + -1) + -8m + 9

Reorder the terms:
16 + -6m + 6m + -6m2 = 4m + -1(2m + -1) + -8m + 9

Combine like terms: -6m + 6m = 0
16 + 0 + -6m2 = 4m + -1(2m + -1) + -8m + 9
16 + -6m2 = 4m + -1(2m + -1) + -8m + 9

Reorder the terms:
16 + -6m2 = 4m + -1(-1 + 2m) + -8m + 9
16 + -6m2 = 4m + (-1 * -1 + 2m * -1) + -8m + 9
16 + -6m2 = 4m + (1 + -2m) + -8m + 9

Reorder the terms:
16 + -6m2 = 1 + 9 + 4m + -2m + -8m

Combine like terms: 1 + 9 = 10
16 + -6m2 = 10 + 4m + -2m + -8m

Combine like terms: 4m + -2m = 2m
16 + -6m2 = 10 + 2m + -8m

Combine like terms: 2m + -8m = -6m
16 + -6m2 = 10 + -6m

Solving
16 + -6m2 = 10 + -6m

Solving for variable 'm'.

Reorder the terms:
16 + -10 + 6m + -6m2 = 10 + -6m + -10 + 6m

Combine like terms: 16 + -10 = 6
6 + 6m + -6m2 = 10 + -6m + -10 + 6m

Reorder the terms:
6 + 6m + -6m2 = 10 + -10 + -6m + 6m

Combine like terms: 10 + -10 = 0
6 + 6m + -6m2 = 0 + -6m + 6m
6 + 6m + -6m2 = -6m + 6m

Combine like terms: -6m + 6m = 0
6 + 6m + -6m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + m + -1m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + m + -1m2)' equal to zero and attempt to solve:

Simplifying
1 + m + -1m2 = 0

Solving
1 + m + -1m2 = 0

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

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

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -1m + m2 = 0 + 1

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

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

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 1 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1m + m2 = 1.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(m + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
m + 0.5 = 1.118033989

Simplifying
m + 0.5 = 1.118033989

Reorder the terms:
0.5 + m = 1.118033989

Solving
0.5 + m = 1.118033989

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 1.118033989 + -0.5
m = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
m = 0.618033989

Simplifying
m = 0.618033989

Subproblem 2
m + 0.5 = -1.118033989

Simplifying
m + 0.5 = -1.118033989

Reorder the terms:
0.5 + m = -1.118033989

Solving
0.5 + m = -1.118033989

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -1.118033989 + -0.5
m = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
m = -1.618033989

Simplifying
m = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.618033989, -1.618033989}
Solution
m = {0.618033989, -1.618033989}