2(m-3)=(m+4)(m-6)

Solution for 2(m-3)=(m+4)(m-6) equation:

Simplifying
2(m + -3) = (m + 4)(m + -6)

Reorder the terms:
2(-3 + m) = (m + 4)(m + -6)
(-3 * 2 + m * 2) = (m + 4)(m + -6)
(-6 + 2m) = (m + 4)(m + -6)

Reorder the terms:
-6 + 2m = (4 + m)(m + -6)

Reorder the terms:
-6 + 2m = (4 + m)(-6 + m)

Multiply (4 + m) * (-6 + m)
-6 + 2m = (4(-6 + m) + m(-6 + m))
-6 + 2m = ((-6 * 4 + m * 4) + m(-6 + m))
-6 + 2m = ((-24 + 4m) + m(-6 + m))
-6 + 2m = (-24 + 4m + (-6 * m + m * m))
-6 + 2m = (-24 + 4m + (-6m + m2))

Combine like terms: 4m + -6m = -2m
-6 + 2m = (-24 + -2m + m2)

Solving
-6 + 2m = -24 + -2m + m2

Solving for variable 'm'.

Reorder the terms:
-6 + 24 + 2m + 2m + -1m2 = -24 + -2m + m2 + 24 + 2m + -1m2

Combine like terms: -6 + 24 = 18
18 + 2m + 2m + -1m2 = -24 + -2m + m2 + 24 + 2m + -1m2

Combine like terms: 2m + 2m = 4m
18 + 4m + -1m2 = -24 + -2m + m2 + 24 + 2m + -1m2

Reorder the terms:
18 + 4m + -1m2 = -24 + 24 + -2m + 2m + m2 + -1m2

Combine like terms: -24 + 24 = 0
18 + 4m + -1m2 = 0 + -2m + 2m + m2 + -1m2
18 + 4m + -1m2 = -2m + 2m + m2 + -1m2

Combine like terms: -2m + 2m = 0
18 + 4m + -1m2 = 0 + m2 + -1m2
18 + 4m + -1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
18 + 4m + -1m2 = 0

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

Divide each side by '-1'.
-18 + -4m + m2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -4m + 18 + m2 = 0 + 18

Reorder the terms:
-18 + 18 + -4m + m2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -4m + m2 = 0 + 18
-4m + m2 = 0 + 18

Combine like terms: 0 + 18 = 18
-4m + m2 = 18

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 18 + 4

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

Combine like terms: 18 + 4 = 22
4 + -4m + m2 = 22

Factor a perfect square on the left side:
(m + -2)(m + -2) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(m + -2) equal to 4.69041576 and -4.69041576.

Subproblem 1
m + -2 = 4.69041576

Simplifying
m + -2 = 4.69041576

Reorder the terms:
-2 + m = 4.69041576

Solving
-2 + m = 4.69041576

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = 4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + m = 4.69041576 + 2
m = 4.69041576 + 2

Combine like terms: 4.69041576 + 2 = 6.69041576
m = 6.69041576

Simplifying
m = 6.69041576

Subproblem 2
m + -2 = -4.69041576

Simplifying
m + -2 = -4.69041576

Reorder the terms:
-2 + m = -4.69041576

Solving
-2 + m = -4.69041576

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = -4.69041576 + 2

Combine like terms: -2 + 2 = 0
0 + m = -4.69041576 + 2
m = -4.69041576 + 2

Combine like terms: -4.69041576 + 2 = -2.69041576
m = -2.69041576

Simplifying
m = -2.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.69041576, -2.69041576}