3m^2(8-m)+m(m+3)=

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

Simplifying
3m2(8 + -1m) + m(m + 3) = 0
(8 * 3m2 + -1m * 3m2) + m(m + 3) = 0
(24m2 + -3m3) + m(m + 3) = 0

Reorder the terms:
24m2 + -3m3 + m(3 + m) = 0
24m2 + -3m3 + (3 * m + m * m) = 0
24m2 + -3m3 + (3m + m2) = 0

Reorder the terms:
3m + 24m2 + m2 + -3m3 = 0

Combine like terms: 24m2 + m2 = 25m2
3m + 25m2 + -3m3 = 0

Solving
3m + 25m2 + -3m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(3 + 25m + -3m2) = 0

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(3 + 25m + -3m2)' equal to zero and attempt to solve:

Simplifying
3 + 25m + -3m2 = 0

Solving
3 + 25m + -3m2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + -8.333333333m + m2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -8.333333333m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -8.333333333m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8.333333333m + m2 = 0 + 1
-8.333333333m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-8.333333333m + m2 = 1

The m term is -8.333333333m.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333m + 17.36111111 + m2 = 1 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333m + m2 = 1 + 17.36111111

Combine like terms: 1 + 17.36111111 = 18.36111111
17.36111111 + -8.333333333m + m2 = 18.36111111

Factor a perfect square on the left side:
(m + -4.166666667)(m + -4.166666667) = 18.36111111

Calculate the square root of the right side: 4.284986711

Break this problem into two subproblems by setting 
(m + -4.166666667) equal to 4.284986711 and -4.284986711.

Subproblem 1
m + -4.166666667 = 4.284986711

Simplifying
m + -4.166666667 = 4.284986711

Reorder the terms:
-4.166666667 + m = 4.284986711

Solving
-4.166666667 + m = 4.284986711

Solving for variable 'm'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + m = 4.284986711 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + m = 4.284986711 + 4.166666667
m = 4.284986711 + 4.166666667

Combine like terms: 4.284986711 + 4.166666667 = 8.451653378
m = 8.451653378

Simplifying
m = 8.451653378

Subproblem 2
m + -4.166666667 = -4.284986711

Simplifying
m + -4.166666667 = -4.284986711

Reorder the terms:
-4.166666667 + m = -4.284986711

Solving
-4.166666667 + m = -4.284986711

Solving for variable 'm'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + m = -4.284986711 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + m = -4.284986711 + 4.166666667
m = -4.284986711 + 4.166666667

Combine like terms: -4.284986711 + 4.166666667 = -0.118320044
m = -0.118320044

Simplifying
m = -0.118320044

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.451653378, -0.118320044}
Solution
m = {0, 8.451653378, -0.118320044}