6m^2+72m=162

Solution for 6m^2+72m=162 equation:

Simplifying
6m2 + 72m = 162

Reorder the terms:
72m + 6m2 = 162

Solving
72m + 6m2 = 162

Solving for variable 'm'.

Reorder the terms:
-162 + 72m + 6m2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + 72m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-27 + 12m + m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-27 + 12m + m2)' equal to zero and attempt to solve:

Simplifying
-27 + 12m + m2 = 0

Solving
-27 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 12m + 27 + m2 = 0 + 27

Reorder the terms:
-27 + 27 + 12m + m2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 12m + m2 = 0 + 27
12m + m2 = 0 + 27

Combine like terms: 0 + 27 = 27
12m + m2 = 27

The m term is 12m.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12m + 36 + m2 = 27 + 36

Reorder the terms:
36 + 12m + m2 = 27 + 36

Combine like terms: 27 + 36 = 63
36 + 12m + m2 = 63

Factor a perfect square on the left side:
(m + 6)(m + 6) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(m + 6) equal to 7.937253933 and -7.937253933.

Subproblem 1
m + 6 = 7.937253933

Simplifying
m + 6 = 7.937253933

Reorder the terms:
6 + m = 7.937253933

Solving
6 + m = 7.937253933

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = 7.937253933 + -6

Combine like terms: 6 + -6 = 0
0 + m = 7.937253933 + -6
m = 7.937253933 + -6

Combine like terms: 7.937253933 + -6 = 1.937253933
m = 1.937253933

Simplifying
m = 1.937253933

Subproblem 2
m + 6 = -7.937253933

Simplifying
m + 6 = -7.937253933

Reorder the terms:
6 + m = -7.937253933

Solving
6 + m = -7.937253933

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = -7.937253933 + -6

Combine like terms: 6 + -6 = 0
0 + m = -7.937253933 + -6
m = -7.937253933 + -6

Combine like terms: -7.937253933 + -6 = -13.937253933
m = -13.937253933

Simplifying
m = -13.937253933

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.937253933, -13.937253933}
Solution
m = {1.937253933, -13.937253933}