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

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

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

Reorder the terms:
3m = 5m(3 + m) + -3
3m = (3 * 5m + m * 5m) + -3
3m = (15m + 5m2) + -3

Reorder the terms:
3m = -3 + 15m + 5m2

Solving
3m = -3 + 15m + 5m2

Solving for variable 'm'.

Reorder the terms:
3 + 3m + -15m + -5m2 = -3 + 15m + 5m2 + 3 + -15m + -5m2

Combine like terms: 3m + -15m = -12m
3 + -12m + -5m2 = -3 + 15m + 5m2 + 3 + -15m + -5m2

Reorder the terms:
3 + -12m + -5m2 = -3 + 3 + 15m + -15m + 5m2 + -5m2

Combine like terms: -3 + 3 = 0
3 + -12m + -5m2 = 0 + 15m + -15m + 5m2 + -5m2
3 + -12m + -5m2 = 15m + -15m + 5m2 + -5m2

Combine like terms: 15m + -15m = 0
3 + -12m + -5m2 = 0 + 5m2 + -5m2
3 + -12m + -5m2 = 5m2 + -5m2

Combine like terms: 5m2 + -5m2 = 0
3 + -12m + -5m2 = 0

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

Divide each side by '-5'.
-0.6 + 2.4m + m2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2.4m + 0.6 + m2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2.4m + m2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2.4m + m2 = 0 + 0.6
2.4m + m2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2.4m + m2 = 0.6

The m term is 2.4m.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4m + 1.44 + m2 = 0.6 + 1.44

Reorder the terms:
1.44 + 2.4m + m2 = 0.6 + 1.44

Combine like terms: 0.6 + 1.44 = 2.04
1.44 + 2.4m + m2 = 2.04

Factor a perfect square on the left side:
(m + 1.2)(m + 1.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(m + 1.2) equal to 1.428285686 and -1.428285686.

Subproblem 1
m + 1.2 = 1.428285686

Simplifying
m + 1.2 = 1.428285686

Reorder the terms:
1.2 + m = 1.428285686

Solving
1.2 + m = 1.428285686

Solving for variable 'm'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + m = 1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + m = 1.428285686 + -1.2
m = 1.428285686 + -1.2

Combine like terms: 1.428285686 + -1.2 = 0.228285686
m = 0.228285686

Simplifying
m = 0.228285686

Subproblem 2
m + 1.2 = -1.428285686

Simplifying
m + 1.2 = -1.428285686

Reorder the terms:
1.2 + m = -1.428285686

Solving
1.2 + m = -1.428285686

Solving for variable 'm'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + m = -1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + m = -1.428285686 + -1.2
m = -1.428285686 + -1.2

Combine like terms: -1.428285686 + -1.2 = -2.628285686
m = -2.628285686

Simplifying
m = -2.628285686

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.228285686, -2.628285686}