3m(2m+4)=30

Solution for 3m(2m+4)=30 equation:

Simplifying
3m(2m + 4) = 30

Reorder the terms:
3m(4 + 2m) = 30
(4 * 3m + 2m * 3m) = 30
(12m + 6m2) = 30

Solving
12m + 6m2 = 30

Solving for variable 'm'.

Reorder the terms:
-30 + 12m + 6m2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 12m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 2m + m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 2m + m2)' equal to zero and attempt to solve:

Simplifying
-5 + 2m + m2 = 0

Solving
-5 + 2m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2m + 5 + m2 = 0 + 5

Reorder the terms:
-5 + 5 + 2m + m2 = 0 + 5

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

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

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = 5 + 1

Reorder the terms:
1 + 2m + m2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2m + m2 = 6

Factor a perfect square on the left side:
(m + 1)(m + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(m + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1
m + 1 = 2.449489743

Simplifying
m + 1 = 2.449489743

Reorder the terms:
1 + m = 2.449489743

Solving
1 + m = 2.449489743

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + m = 2.449489743 + -1
m = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
m = 1.449489743

Simplifying
m = 1.449489743

Subproblem 2
m + 1 = -2.449489743

Simplifying
m + 1 = -2.449489743

Reorder the terms:
1 + m = -2.449489743

Solving
1 + m = -2.449489743

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + m = -2.449489743 + -1
m = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
m = -3.449489743

Simplifying
m = -3.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.449489743, -3.449489743}
Solution
m = {1.449489743, -3.449489743}