3m(8+3m)=4(m+2)-4+6

Solution for 3m(8+3m)=4(m+2)-4+6 equation:

Simplifying
3m(8 + 3m) = 4(m + 2) + -4 + 6
(8 * 3m + 3m * 3m) = 4(m + 2) + -4 + 6
(24m + 9m2) = 4(m + 2) + -4 + 6

Reorder the terms:
24m + 9m2 = 4(2 + m) + -4 + 6
24m + 9m2 = (2 * 4 + m * 4) + -4 + 6
24m + 9m2 = (8 + 4m) + -4 + 6

Reorder the terms:
24m + 9m2 = 8 + -4 + 6 + 4m

Combine like terms: 8 + -4 = 4
24m + 9m2 = 4 + 6 + 4m

Combine like terms: 4 + 6 = 10
24m + 9m2 = 10 + 4m

Solving
24m + 9m2 = 10 + 4m

Solving for variable 'm'.

Reorder the terms:
-10 + 24m + -4m + 9m2 = 10 + 4m + -10 + -4m

Combine like terms: 24m + -4m = 20m
-10 + 20m + 9m2 = 10 + 4m + -10 + -4m

Reorder the terms:
-10 + 20m + 9m2 = 10 + -10 + 4m + -4m

Combine like terms: 10 + -10 = 0
-10 + 20m + 9m2 = 0 + 4m + -4m
-10 + 20m + 9m2 = 4m + -4m

Combine like terms: 4m + -4m = 0
-10 + 20m + 9m2 = 0

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

Divide each side by '9'.
-1.111111111 + 2.222222222m + m2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 2.222222222m + 1.111111111 + m2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 2.222222222m + m2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 2.222222222m + m2 = 0 + 1.111111111
2.222222222m + m2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
2.222222222m + m2 = 1.111111111

The m term is 2.222222222m.  Take half its coefficient (1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
2.222222222m + 1.234567901 + m2 = 1.111111111 + 1.234567901

Reorder the terms:
1.234567901 + 2.222222222m + m2 = 1.111111111 + 1.234567901

Combine like terms: 1.111111111 + 1.234567901 = 2.345679012
1.234567901 + 2.222222222m + m2 = 2.345679012

Factor a perfect square on the left side:
(m + 1.111111111)(m + 1.111111111) = 2.345679012

Calculate the square root of the right side: 1.531560972

Break this problem into two subproblems by setting 
(m + 1.111111111) equal to 1.531560972 and -1.531560972.

Subproblem 1
m + 1.111111111 = 1.531560972

Simplifying
m + 1.111111111 = 1.531560972

Reorder the terms:
1.111111111 + m = 1.531560972

Solving
1.111111111 + m = 1.531560972

Solving for variable 'm'.

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

Add '-1.111111111' to each side of the equation.
1.111111111 + -1.111111111 + m = 1.531560972 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + m = 1.531560972 + -1.111111111
m = 1.531560972 + -1.111111111

Combine like terms: 1.531560972 + -1.111111111 = 0.420449861
m = 0.420449861

Simplifying
m = 0.420449861

Subproblem 2
m + 1.111111111 = -1.531560972

Simplifying
m + 1.111111111 = -1.531560972

Reorder the terms:
1.111111111 + m = -1.531560972

Solving
1.111111111 + m = -1.531560972

Solving for variable 'm'.

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

Add '-1.111111111' to each side of the equation.
1.111111111 + -1.111111111 + m = -1.531560972 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + m = -1.531560972 + -1.111111111
m = -1.531560972 + -1.111111111

Combine like terms: -1.531560972 + -1.111111111 = -2.642672083
m = -2.642672083

Simplifying
m = -2.642672083

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.420449861, -2.642672083}