-2m(m-9)=4m-6

Solution for -2m(m-9)=4m-6 equation:

Simplifying
-2m(m + -9) = 4m + -6

Reorder the terms:
-2m(-9 + m) = 4m + -6
(-9 * -2m + m * -2m) = 4m + -6
(18m + -2m2) = 4m + -6

Reorder the terms:
18m + -2m2 = -6 + 4m

Solving
18m + -2m2 = -6 + 4m

Solving for variable 'm'.

Reorder the terms:
6 + 18m + -4m + -2m2 = -6 + 4m + 6 + -4m

Combine like terms: 18m + -4m = 14m
6 + 14m + -2m2 = -6 + 4m + 6 + -4m

Reorder the terms:
6 + 14m + -2m2 = -6 + 6 + 4m + -4m

Combine like terms: -6 + 6 = 0
6 + 14m + -2m2 = 0 + 4m + -4m
6 + 14m + -2m2 = 4m + -4m

Combine like terms: 4m + -4m = 0
6 + 14m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7m + -1m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 7m + -1m2)' equal to zero and attempt to solve:

Simplifying
3 + 7m + -1m2 = 0

Solving
3 + 7m + -1m2 = 0

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

Divide each side by '-1'.
-3 + -7m + m2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -7m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + -7m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7m + m2 = 0 + 3
-7m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-7m + m2 = 3

The m term is -7m.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7m + 12.25 + m2 = 3 + 12.25

Reorder the terms:
12.25 + -7m + m2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + -7m + m2 = 15.25

Factor a perfect square on the left side:
(m + -3.5)(m + -3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(m + -3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
m + -3.5 = 3.905124838

Simplifying
m + -3.5 = 3.905124838

Reorder the terms:
-3.5 + m = 3.905124838

Solving
-3.5 + m = 3.905124838

Solving for variable 'm'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + m = 3.905124838 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + m = 3.905124838 + 3.5
m = 3.905124838 + 3.5

Combine like terms: 3.905124838 + 3.5 = 7.405124838
m = 7.405124838

Simplifying
m = 7.405124838

Subproblem 2
m + -3.5 = -3.905124838

Simplifying
m + -3.5 = -3.905124838

Reorder the terms:
-3.5 + m = -3.905124838

Solving
-3.5 + m = -3.905124838

Solving for variable 'm'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + m = -3.905124838 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + m = -3.905124838 + 3.5
m = -3.905124838 + 3.5

Combine like terms: -3.905124838 + 3.5 = -0.405124838
m = -0.405124838

Simplifying
m = -0.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.405124838, -0.405124838}
Solution
m = {7.405124838, -0.405124838}