3m(m+3)=420

Solution for 3m(m+3)=420 equation:

Simplifying
3m(m + 3) = 420

Reorder the terms:
3m(3 + m) = 420
(3 * 3m + m * 3m) = 420
(9m + 3m2) = 420

Solving
9m + 3m2 = 420

Solving for variable 'm'.

Reorder the terms:
-420 + 9m + 3m2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + 9m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-140 + 3m + m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-140 + 3m + m2)' equal to zero and attempt to solve:

Simplifying
-140 + 3m + m2 = 0

Solving
-140 + 3m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 3m + 140 + m2 = 0 + 140

Reorder the terms:
-140 + 140 + 3m + m2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 3m + m2 = 0 + 140
3m + m2 = 0 + 140

Combine like terms: 0 + 140 = 140
3m + m2 = 140

The m term is 3m.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3m + 2.25 + m2 = 140 + 2.25

Reorder the terms:
2.25 + 3m + m2 = 140 + 2.25

Combine like terms: 140 + 2.25 = 142.25
2.25 + 3m + m2 = 142.25

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(m + 1.5) equal to 11.926860442 and -11.926860442.

Subproblem 1
m + 1.5 = 11.926860442

Simplifying
m + 1.5 = 11.926860442

Reorder the terms:
1.5 + m = 11.926860442

Solving
1.5 + m = 11.926860442

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = 11.926860442 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = 11.926860442 + -1.5
m = 11.926860442 + -1.5

Combine like terms: 11.926860442 + -1.5 = 10.426860442
m = 10.426860442

Simplifying
m = 10.426860442

Subproblem 2
m + 1.5 = -11.926860442

Simplifying
m + 1.5 = -11.926860442

Reorder the terms:
1.5 + m = -11.926860442

Solving
1.5 + m = -11.926860442

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = -11.926860442 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = -11.926860442 + -1.5
m = -11.926860442 + -1.5

Combine like terms: -11.926860442 + -1.5 = -13.426860442
m = -13.426860442

Simplifying
m = -13.426860442

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {10.426860442, -13.426860442}
Solution
m = {10.426860442, -13.426860442}