3m(2m-9+6m)=3m+29-7m

Solution for 3m(2m-9+6m)=3m+29-7m equation:

Simplifying
3m(2m + -9 + 6m) = 3m + 29 + -7m

Reorder the terms:
3m(-9 + 2m + 6m) = 3m + 29 + -7m

Combine like terms: 2m + 6m = 8m
3m(-9 + 8m) = 3m + 29 + -7m
(-9 * 3m + 8m * 3m) = 3m + 29 + -7m
(-27m + 24m2) = 3m + 29 + -7m

Reorder the terms:
-27m + 24m2 = 29 + 3m + -7m

Combine like terms: 3m + -7m = -4m
-27m + 24m2 = 29 + -4m

Solving
-27m + 24m2 = 29 + -4m

Solving for variable 'm'.

Reorder the terms:
-29 + -27m + 4m + 24m2 = 29 + -4m + -29 + 4m

Combine like terms: -27m + 4m = -23m
-29 + -23m + 24m2 = 29 + -4m + -29 + 4m

Reorder the terms:
-29 + -23m + 24m2 = 29 + -29 + -4m + 4m

Combine like terms: 29 + -29 = 0
-29 + -23m + 24m2 = 0 + -4m + 4m
-29 + -23m + 24m2 = -4m + 4m

Combine like terms: -4m + 4m = 0
-29 + -23m + 24m2 = 0

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

Divide each side by '24'.
-1.208333333 + -0.9583333333m + m2 = 0

Move the constant term to the right:

Add '1.208333333' to each side of the equation.
-1.208333333 + -0.9583333333m + 1.208333333 + m2 = 0 + 1.208333333

Reorder the terms:
-1.208333333 + 1.208333333 + -0.9583333333m + m2 = 0 + 1.208333333

Combine like terms: -1.208333333 + 1.208333333 = 0.000000000
0.000000000 + -0.9583333333m + m2 = 0 + 1.208333333
-0.9583333333m + m2 = 0 + 1.208333333

Combine like terms: 0 + 1.208333333 = 1.208333333
-0.9583333333m + m2 = 1.208333333

The m term is -0.9583333333m.  Take half its coefficient (-0.4791666667).
Square it (0.2296006945) and add it to both sides.

Add '0.2296006945' to each side of the equation.
-0.9583333333m + 0.2296006945 + m2 = 1.208333333 + 0.2296006945

Reorder the terms:
0.2296006945 + -0.9583333333m + m2 = 1.208333333 + 0.2296006945

Combine like terms: 1.208333333 + 0.2296006945 = 1.4379340275
0.2296006945 + -0.9583333333m + m2 = 1.4379340275

Factor a perfect square on the left side:
(m + -0.4791666667)(m + -0.4791666667) = 1.4379340275

Calculate the square root of the right side: 1.199138869

Break this problem into two subproblems by setting 
(m + -0.4791666667) equal to 1.199138869 and -1.199138869.

Subproblem 1
m + -0.4791666667 = 1.199138869

Simplifying
m + -0.4791666667 = 1.199138869

Reorder the terms:
-0.4791666667 + m = 1.199138869

Solving
-0.4791666667 + m = 1.199138869

Solving for variable 'm'.

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

Add '0.4791666667' to each side of the equation.
-0.4791666667 + 0.4791666667 + m = 1.199138869 + 0.4791666667

Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000
0.0000000000 + m = 1.199138869 + 0.4791666667
m = 1.199138869 + 0.4791666667

Combine like terms: 1.199138869 + 0.4791666667 = 1.6783055357
m = 1.6783055357

Simplifying
m = 1.6783055357

Subproblem 2
m + -0.4791666667 = -1.199138869

Simplifying
m + -0.4791666667 = -1.199138869

Reorder the terms:
-0.4791666667 + m = -1.199138869

Solving
-0.4791666667 + m = -1.199138869

Solving for variable 'm'.

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

Add '0.4791666667' to each side of the equation.
-0.4791666667 + 0.4791666667 + m = -1.199138869 + 0.4791666667

Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000
0.0000000000 + m = -1.199138869 + 0.4791666667
m = -1.199138869 + 0.4791666667

Combine like terms: -1.199138869 + 0.4791666667 = -0.7199722023
m = -0.7199722023

Simplifying
m = -0.7199722023

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.6783055357, -0.7199722023}