6m(15m+6)=78

Solution for 6m(15m+6)=78 equation:

Simplifying
6m(15m + 6) = 78

Reorder the terms:
6m(6 + 15m) = 78
(6 * 6m + 15m * 6m) = 78
(36m + 90m2) = 78

Solving
36m + 90m2 = 78

Solving for variable 'm'.

Reorder the terms:
-78 + 36m + 90m2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 36m + 90m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-13 + 6m + 15m2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-13 + 6m + 15m2)' equal to zero and attempt to solve:

Simplifying
-13 + 6m + 15m2 = 0

Solving
-13 + 6m + 15m2 = 0

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

Divide each side by '15'.
-0.8666666667 + 0.4m + m2 = 0

Move the constant term to the right:

Add '0.8666666667' to each side of the equation.
-0.8666666667 + 0.4m + 0.8666666667 + m2 = 0 + 0.8666666667

Reorder the terms:
-0.8666666667 + 0.8666666667 + 0.4m + m2 = 0 + 0.8666666667

Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000
0.0000000000 + 0.4m + m2 = 0 + 0.8666666667
0.4m + m2 = 0 + 0.8666666667

Combine like terms: 0 + 0.8666666667 = 0.8666666667
0.4m + m2 = 0.8666666667

The m term is 0.4m.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4m + 0.04 + m2 = 0.8666666667 + 0.04

Reorder the terms:
0.04 + 0.4m + m2 = 0.8666666667 + 0.04

Combine like terms: 0.8666666667 + 0.04 = 0.9066666667
0.04 + 0.4m + m2 = 0.9066666667

Factor a perfect square on the left side:
(m + 0.2)(m + 0.2) = 0.9066666667

Calculate the square root of the right side: 0.952190457

Break this problem into two subproblems by setting 
(m + 0.2) equal to 0.952190457 and -0.952190457.

Subproblem 1
m + 0.2 = 0.952190457

Simplifying
m + 0.2 = 0.952190457

Reorder the terms:
0.2 + m = 0.952190457

Solving
0.2 + m = 0.952190457

Solving for variable 'm'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + m = 0.952190457 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + m = 0.952190457 + -0.2
m = 0.952190457 + -0.2

Combine like terms: 0.952190457 + -0.2 = 0.752190457
m = 0.752190457

Simplifying
m = 0.752190457

Subproblem 2
m + 0.2 = -0.952190457

Simplifying
m + 0.2 = -0.952190457

Reorder the terms:
0.2 + m = -0.952190457

Solving
0.2 + m = -0.952190457

Solving for variable 'm'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + m = -0.952190457 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + m = -0.952190457 + -0.2
m = -0.952190457 + -0.2

Combine like terms: -0.952190457 + -0.2 = -1.152190457
m = -1.152190457

Simplifying
m = -1.152190457

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.752190457, -1.152190457}
Solution
m = {0.752190457, -1.152190457}