5(1+3m)=10m(m-1)

Solution for 5(1+3m)=10m(m-1) equation:

Simplifying
5(1 + 3m) = 10m(m + -1)
(1 * 5 + 3m * 5) = 10m(m + -1)
(5 + 15m) = 10m(m + -1)

Reorder the terms:
5 + 15m = 10m(-1 + m)
5 + 15m = (-1 * 10m + m * 10m)
5 + 15m = (-10m + 10m2)

Solving
5 + 15m = -10m + 10m2

Solving for variable 'm'.

Combine like terms: 15m + 10m = 25m
5 + 25m + -10m2 = -10m + 10m2 + 10m + -10m2

Reorder the terms:
5 + 25m + -10m2 = -10m + 10m + 10m2 + -10m2

Combine like terms: -10m + 10m = 0
5 + 25m + -10m2 = 0 + 10m2 + -10m2
5 + 25m + -10m2 = 10m2 + -10m2

Combine like terms: 10m2 + -10m2 = 0
5 + 25m + -10m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 5m + -2m2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + 5m + -2m2)' equal to zero and attempt to solve:

Simplifying
1 + 5m + -2m2 = 0

Solving
1 + 5m + -2m2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + -2.5m + m2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2.5m + 0.5 + m2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2.5m + m2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2.5m + m2 = 0 + 0.5
-2.5m + m2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2.5m + m2 = 0.5

The m term is -2.5m.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5m + 1.5625 + m2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + -2.5m + m2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + -2.5m + m2 = 2.0625

Factor a perfect square on the left side:
(m + -1.25)(m + -1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(m + -1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
m + -1.25 = 1.436140662

Simplifying
m + -1.25 = 1.436140662

Reorder the terms:
-1.25 + m = 1.436140662

Solving
-1.25 + m = 1.436140662

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = 1.436140662 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = 1.436140662 + 1.25
m = 1.436140662 + 1.25

Combine like terms: 1.436140662 + 1.25 = 2.686140662
m = 2.686140662

Simplifying
m = 2.686140662

Subproblem 2
m + -1.25 = -1.436140662

Simplifying
m + -1.25 = -1.436140662

Reorder the terms:
-1.25 + m = -1.436140662

Solving
-1.25 + m = -1.436140662

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = -1.436140662 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = -1.436140662 + 1.25
m = -1.436140662 + 1.25

Combine like terms: -1.436140662 + 1.25 = -0.186140662
m = -0.186140662

Simplifying
m = -0.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.686140662, -0.186140662}
Solution
m = {2.686140662, -0.186140662}