(m-2)(-20+2m)=24

Solution for (m-2)(-20+2m)=24 equation:

Simplifying
(m + -2)(-20 + 2m) = 24

Reorder the terms:
(-2 + m)(-20 + 2m) = 24

Multiply (-2 + m) * (-20 + 2m)
(-2(-20 + 2m) + m(-20 + 2m)) = 24
((-20 * -2 + 2m * -2) + m(-20 + 2m)) = 24
((40 + -4m) + m(-20 + 2m)) = 24
(40 + -4m + (-20 * m + 2m * m)) = 24
(40 + -4m + (-20m + 2m2)) = 24

Combine like terms: -4m + -20m = -24m
(40 + -24m + 2m2) = 24

Solving
40 + -24m + 2m2 = 24

Solving for variable 'm'.

Reorder the terms:
40 + -24 + -24m + 2m2 = 24 + -24

Combine like terms: 40 + -24 = 16
16 + -24m + 2m2 = 24 + -24

Combine like terms: 24 + -24 = 0
16 + -24m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -12m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -12m + m2)' equal to zero and attempt to solve:

Simplifying
8 + -12m + m2 = 0

Solving
8 + -12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -12m + -8 + m2 = 0 + -8

Reorder the terms:
8 + -8 + -12m + m2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -12m + m2 = 0 + -8
-12m + m2 = 0 + -8

Combine like terms: 0 + -8 = -8
-12m + m2 = -8

The m term is -12m.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12m + 36 + m2 = -8 + 36

Reorder the terms:
36 + -12m + m2 = -8 + 36

Combine like terms: -8 + 36 = 28
36 + -12m + m2 = 28

Factor a perfect square on the left side:
(m + -6)(m + -6) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(m + -6) equal to 5.291502622 and -5.291502622.

Subproblem 1
m + -6 = 5.291502622

Simplifying
m + -6 = 5.291502622

Reorder the terms:
-6 + m = 5.291502622

Solving
-6 + m = 5.291502622

Solving for variable 'm'.

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

Add '6' to each side of the equation.
-6 + 6 + m = 5.291502622 + 6

Combine like terms: -6 + 6 = 0
0 + m = 5.291502622 + 6
m = 5.291502622 + 6

Combine like terms: 5.291502622 + 6 = 11.291502622
m = 11.291502622

Simplifying
m = 11.291502622

Subproblem 2
m + -6 = -5.291502622

Simplifying
m + -6 = -5.291502622

Reorder the terms:
-6 + m = -5.291502622

Solving
-6 + m = -5.291502622

Solving for variable 'm'.

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

Add '6' to each side of the equation.
-6 + 6 + m = -5.291502622 + 6

Combine like terms: -6 + 6 = 0
0 + m = -5.291502622 + 6
m = -5.291502622 + 6

Combine like terms: -5.291502622 + 6 = 0.708497378
m = 0.708497378

Simplifying
m = 0.708497378

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {11.291502622, 0.708497378}
Solution
m = {11.291502622, 0.708497378}