8m(m-5)=2(3m-8)

Solution for 8m(m-5)=2(3m-8) equation:

Simplifying
8m(m + -5) = 2(3m + -8)

Reorder the terms:
8m(-5 + m) = 2(3m + -8)
(-5 * 8m + m * 8m) = 2(3m + -8)
(-40m + 8m2) = 2(3m + -8)

Reorder the terms:
-40m + 8m2 = 2(-8 + 3m)
-40m + 8m2 = (-8 * 2 + 3m * 2)
-40m + 8m2 = (-16 + 6m)

Solving
-40m + 8m2 = -16 + 6m

Solving for variable 'm'.

Reorder the terms:
16 + -40m + -6m + 8m2 = -16 + 6m + 16 + -6m

Combine like terms: -40m + -6m = -46m
16 + -46m + 8m2 = -16 + 6m + 16 + -6m

Reorder the terms:
16 + -46m + 8m2 = -16 + 16 + 6m + -6m

Combine like terms: -16 + 16 = 0
16 + -46m + 8m2 = 0 + 6m + -6m
16 + -46m + 8m2 = 6m + -6m

Combine like terms: 6m + -6m = 0
16 + -46m + 8m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -23m + 4m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -23m + 4m2)' equal to zero and attempt to solve:

Simplifying
8 + -23m + 4m2 = 0

Solving
8 + -23m + 4m2 = 0

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

Divide each side by '4'.
2 + -5.75m + m2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5.75m + -2 + m2 = 0 + -2

Reorder the terms:
2 + -2 + -5.75m + m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5.75m + m2 = 0 + -2
-5.75m + m2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5.75m + m2 = -2

The m term is -5.75m.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75m + 8.265625 + m2 = -2 + 8.265625

Reorder the terms:
8.265625 + -5.75m + m2 = -2 + 8.265625

Combine like terms: -2 + 8.265625 = 6.265625
8.265625 + -5.75m + m2 = 6.265625

Factor a perfect square on the left side:
(m + -2.875)(m + -2.875) = 6.265625

Calculate the square root of the right side: 2.503123049

Break this problem into two subproblems by setting 
(m + -2.875) equal to 2.503123049 and -2.503123049.

Subproblem 1
m + -2.875 = 2.503123049

Simplifying
m + -2.875 = 2.503123049

Reorder the terms:
-2.875 + m = 2.503123049

Solving
-2.875 + m = 2.503123049

Solving for variable 'm'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + m = 2.503123049 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + m = 2.503123049 + 2.875
m = 2.503123049 + 2.875

Combine like terms: 2.503123049 + 2.875 = 5.378123049
m = 5.378123049

Simplifying
m = 5.378123049

Subproblem 2
m + -2.875 = -2.503123049

Simplifying
m + -2.875 = -2.503123049

Reorder the terms:
-2.875 + m = -2.503123049

Solving
-2.875 + m = -2.503123049

Solving for variable 'm'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + m = -2.503123049 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + m = -2.503123049 + 2.875
m = -2.503123049 + 2.875

Combine like terms: -2.503123049 + 2.875 = 0.371876951
m = 0.371876951

Simplifying
m = 0.371876951

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.378123049, 0.371876951}
Solution
m = {5.378123049, 0.371876951}