5(m-2)m=13

Solution for 5(m-2)m=13 equation:

Simplifying
5(m + -2) * m = 13

Reorder the terms:
5(-2 + m) * m = 13

Reorder the terms for easier multiplication:
5m(-2 + m) = 13
(-2 * 5m + m * 5m) = 13
(-10m + 5m2) = 13

Solving
-10m + 5m2 = 13

Solving for variable 'm'.

Reorder the terms:
-13 + -10m + 5m2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -10m + 5m2 = 0

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

Divide each side by '5'.
-2.6 + -2m + m2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -2m + 2.6 + m2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -2m + m2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -2m + m2 = 0 + 2.6
-2m + m2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-2m + m2 = 2.6

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 2.6 + 1

Reorder the terms:
1 + -2m + m2 = 2.6 + 1

Combine like terms: 2.6 + 1 = 3.6
1 + -2m + m2 = 3.6

Factor a perfect square on the left side:
(m + -1)(m + -1) = 3.6

Calculate the square root of the right side: 1.897366596

Break this problem into two subproblems by setting 
(m + -1) equal to 1.897366596 and -1.897366596.

Subproblem 1
m + -1 = 1.897366596

Simplifying
m + -1 = 1.897366596

Reorder the terms:
-1 + m = 1.897366596

Solving
-1 + m = 1.897366596

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 1.897366596 + 1

Combine like terms: -1 + 1 = 0
0 + m = 1.897366596 + 1
m = 1.897366596 + 1

Combine like terms: 1.897366596 + 1 = 2.897366596
m = 2.897366596

Simplifying
m = 2.897366596

Subproblem 2
m + -1 = -1.897366596

Simplifying
m + -1 = -1.897366596

Reorder the terms:
-1 + m = -1.897366596

Solving
-1 + m = -1.897366596

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -1.897366596 + 1

Combine like terms: -1 + 1 = 0
0 + m = -1.897366596 + 1
m = -1.897366596 + 1

Combine like terms: -1.897366596 + 1 = -0.897366596
m = -0.897366596

Simplifying
m = -0.897366596

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.897366596, -0.897366596}