9+12m=6+15m(m-1)

Solution for 9+12m=6+15m(m-1) equation:

Simplifying
9 + 12m = 6 + 15m(m + -1)

Reorder the terms:
9 + 12m = 6 + 15m(-1 + m)
9 + 12m = 6 + (-1 * 15m + m * 15m)
9 + 12m = 6 + (-15m + 15m2)

Solving
9 + 12m = 6 + -15m + 15m2

Solving for variable 'm'.

Reorder the terms:
9 + -6 + 12m + 15m + -15m2 = 6 + -15m + 15m2 + -6 + 15m + -15m2

Combine like terms: 9 + -6 = 3
3 + 12m + 15m + -15m2 = 6 + -15m + 15m2 + -6 + 15m + -15m2

Combine like terms: 12m + 15m = 27m
3 + 27m + -15m2 = 6 + -15m + 15m2 + -6 + 15m + -15m2

Reorder the terms:
3 + 27m + -15m2 = 6 + -6 + -15m + 15m + 15m2 + -15m2

Combine like terms: 6 + -6 = 0
3 + 27m + -15m2 = 0 + -15m + 15m + 15m2 + -15m2
3 + 27m + -15m2 = -15m + 15m + 15m2 + -15m2

Combine like terms: -15m + 15m = 0
3 + 27m + -15m2 = 0 + 15m2 + -15m2
3 + 27m + -15m2 = 15m2 + -15m2

Combine like terms: 15m2 + -15m2 = 0
3 + 27m + -15m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 9m + -5m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 9m + -5m2)' equal to zero and attempt to solve:

Simplifying
1 + 9m + -5m2 = 0

Solving
1 + 9m + -5m2 = 0

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

Divide each side by '-5'.
-0.2 + -1.8m + m2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.8m + 0.2 + m2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.8m + m2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.8m + m2 = 0 + 0.2
-1.8m + m2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.8m + m2 = 0.2

The m term is -1.8m.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8m + 0.81 + m2 = 0.2 + 0.81

Reorder the terms:
0.81 + -1.8m + m2 = 0.2 + 0.81

Combine like terms: 0.2 + 0.81 = 1.01
0.81 + -1.8m + m2 = 1.01

Factor a perfect square on the left side:
(m + -0.9)(m + -0.9) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(m + -0.9) equal to 1.004987562 and -1.004987562.

Subproblem 1
m + -0.9 = 1.004987562

Simplifying
m + -0.9 = 1.004987562

Reorder the terms:
-0.9 + m = 1.004987562

Solving
-0.9 + m = 1.004987562

Solving for variable 'm'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + m = 1.004987562 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + m = 1.004987562 + 0.9
m = 1.004987562 + 0.9

Combine like terms: 1.004987562 + 0.9 = 1.904987562
m = 1.904987562

Simplifying
m = 1.904987562

Subproblem 2
m + -0.9 = -1.004987562

Simplifying
m + -0.9 = -1.004987562

Reorder the terms:
-0.9 + m = -1.004987562

Solving
-0.9 + m = -1.004987562

Solving for variable 'm'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + m = -1.004987562 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + m = -1.004987562 + 0.9
m = -1.004987562 + 0.9

Combine like terms: -1.004987562 + 0.9 = -0.104987562
m = -0.104987562

Simplifying
m = -0.104987562

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.904987562, -0.104987562}
Solution
m = {1.904987562, -0.104987562}