3m(m-3)*-6(m-5)=2m^2-4m

Solution for 3m(m-3)*-6(m-5)=2m^2-4m equation:

Simplifying
3m(m + -3) * -6(m + -5) = 2m2 + -4m

Reorder the terms:
3m(-3 + m) * -6(m + -5) = 2m2 + -4m

Reorder the terms:
3m(-3 + m) * -6(-5 + m) = 2m2 + -4m

Reorder the terms for easier multiplication:
3 * -6m(-3 + m)(-5 + m) = 2m2 + -4m

Multiply 3 * -6
-18m(-3 + m)(-5 + m) = 2m2 + -4m

Multiply (-3 + m) * (-5 + m)
-18m(-3(-5 + m) + m(-5 + m)) = 2m2 + -4m
-18m((-5 * -3 + m * -3) + m(-5 + m)) = 2m2 + -4m
-18m((15 + -3m) + m(-5 + m)) = 2m2 + -4m
-18m(15 + -3m + (-5 * m + m * m)) = 2m2 + -4m
-18m(15 + -3m + (-5m + m2)) = 2m2 + -4m

Combine like terms: -3m + -5m = -8m
-18m(15 + -8m + m2) = 2m2 + -4m
(15 * -18m + -8m * -18m + m2 * -18m) = 2m2 + -4m
(-270m + 144m2 + -18m3) = 2m2 + -4m

Reorder the terms:
-270m + 144m2 + -18m3 = -4m + 2m2

Solving
-270m + 144m2 + -18m3 = -4m + 2m2

Solving for variable 'm'.

Reorder the terms:
-270m + 4m + 144m2 + -2m2 + -18m3 = -4m + 2m2 + 4m + -2m2

Combine like terms: -270m + 4m = -266m
-266m + 144m2 + -2m2 + -18m3 = -4m + 2m2 + 4m + -2m2

Combine like terms: 144m2 + -2m2 = 142m2
-266m + 142m2 + -18m3 = -4m + 2m2 + 4m + -2m2

Reorder the terms:
-266m + 142m2 + -18m3 = -4m + 4m + 2m2 + -2m2

Combine like terms: -4m + 4m = 0
-266m + 142m2 + -18m3 = 0 + 2m2 + -2m2
-266m + 142m2 + -18m3 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
-266m + 142m2 + -18m3 = 0

Factor out the Greatest Common Factor (GCF), '2m'.
2m(-133 + 71m + -9m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(-133 + 71m + -9m2)' equal to zero and attempt to solve:

Simplifying
-133 + 71m + -9m2 = 0

Solving
-133 + 71m + -9m2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
14.77777778 + -7.888888889m + m2 = 0

Move the constant term to the right:

Add '-14.77777778' to each side of the equation.
14.77777778 + -7.888888889m + -14.77777778 + m2 = 0 + -14.77777778

Reorder the terms:
14.77777778 + -14.77777778 + -7.888888889m + m2 = 0 + -14.77777778

Combine like terms: 14.77777778 + -14.77777778 = 0.00000000
0.00000000 + -7.888888889m + m2 = 0 + -14.77777778
-7.888888889m + m2 = 0 + -14.77777778

Combine like terms: 0 + -14.77777778 = -14.77777778
-7.888888889m + m2 = -14.77777778

The m term is -7.888888889m.  Take half its coefficient (-3.944444445).
Square it (15.55864198) and add it to both sides.

Add '15.55864198' to each side of the equation.
-7.888888889m + 15.55864198 + m2 = -14.77777778 + 15.55864198

Reorder the terms:
15.55864198 + -7.888888889m + m2 = -14.77777778 + 15.55864198

Combine like terms: -14.77777778 + 15.55864198 = 0.7808642
15.55864198 + -7.888888889m + m2 = 0.7808642

Factor a perfect square on the left side:
(m + -3.944444445)(m + -3.944444445) = 0.7808642

Calculate the square root of the right side: 0.883665208

Break this problem into two subproblems by setting 
(m + -3.944444445) equal to 0.883665208 and -0.883665208.

Subproblem 1
m + -3.944444445 = 0.883665208

Simplifying
m + -3.944444445 = 0.883665208

Reorder the terms:
-3.944444445 + m = 0.883665208

Solving
-3.944444445 + m = 0.883665208

Solving for variable 'm'.

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

Add '3.944444445' to each side of the equation.
-3.944444445 + 3.944444445 + m = 0.883665208 + 3.944444445

Combine like terms: -3.944444445 + 3.944444445 = 0.000000000
0.000000000 + m = 0.883665208 + 3.944444445
m = 0.883665208 + 3.944444445

Combine like terms: 0.883665208 + 3.944444445 = 4.828109653
m = 4.828109653

Simplifying
m = 4.828109653

Subproblem 2
m + -3.944444445 = -0.883665208

Simplifying
m + -3.944444445 = -0.883665208

Reorder the terms:
-3.944444445 + m = -0.883665208

Solving
-3.944444445 + m = -0.883665208

Solving for variable 'm'.

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

Add '3.944444445' to each side of the equation.
-3.944444445 + 3.944444445 + m = -0.883665208 + 3.944444445

Combine like terms: -3.944444445 + 3.944444445 = 0.000000000
0.000000000 + m = -0.883665208 + 3.944444445
m = -0.883665208 + 3.944444445

Combine like terms: -0.883665208 + 3.944444445 = 3.060779237
m = 3.060779237

Simplifying
m = 3.060779237

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.828109653, 3.060779237}
Solution
m = {0, 4.828109653, 3.060779237}