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

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


Simplifying
3(m + -3) = m(5 + -1m) + -1m2

Reorder the terms:
3(-3 + m) = m(5 + -1m) + -1m2
(-3 * 3 + m * 3) = m(5 + -1m) + -1m2
(-9 + 3m) = m(5 + -1m) + -1m2
-9 + 3m = (5 * m + -1m * m) + -1m2
-9 + 3m = (5m + -1m2) + -1m2

Combine like terms: -1m2 + -1m2 = -2m2
-9 + 3m = 5m + -2m2

Solving
-9 + 3m = 5m + -2m2

Solving for variable 'm'.

Combine like terms: 3m + -5m = -2m
-9 + -2m + 2m2 = 5m + -2m2 + -5m + 2m2

Reorder the terms:
-9 + -2m + 2m2 = 5m + -5m + -2m2 + 2m2

Combine like terms: 5m + -5m = 0
-9 + -2m + 2m2 = 0 + -2m2 + 2m2
-9 + -2m + 2m2 = -2m2 + 2m2

Combine like terms: -2m2 + 2m2 = 0
-9 + -2m + 2m2 = 0

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

Divide each side by '2'.
-4.5 + -1m + m2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1m + 4.5 + m2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1m + m2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1m + m2 = 0 + 4.5
-1m + m2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1m + m2 = 4.5

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 4.5 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 4.5 + 0.25

Combine like terms: 4.5 + 0.25 = 4.75
0.25 + -1m + m2 = 4.75

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(m + -0.5) equal to 2.179449472 and -2.179449472.


Subproblem 1
m + -0.5 = 2.179449472

Simplifying
m + -0.5 = 2.179449472

Reorder the terms:
-0.5 + m = 2.179449472

Solving
-0.5 + m = 2.179449472

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 2.179449472 + 0.5
m = 2.179449472 + 0.5

Combine like terms: 2.179449472 + 0.5 = 2.679449472
m = 2.679449472

Simplifying
m = 2.679449472


Subproblem 2
m + -0.5 = -2.179449472

Simplifying
m + -0.5 = -2.179449472

Reorder the terms:
-0.5 + m = -2.179449472

Solving
-0.5 + m = -2.179449472

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -2.179449472 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -2.179449472 + 0.5
m = -2.179449472 + 0.5

Combine like terms: -2.179449472 + 0.5 = -1.679449472
m = -1.679449472

Simplifying
m = -1.679449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.679449472, -1.679449472}

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