-3m^2-30m+39=0

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Solution for -3m^2-30m+39=0 equation:


Simplifying
-3m2 + -30m + 39 = 0

Reorder the terms:
39 + -30m + -3m2 = 0

Solving
39 + -30m + -3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + -10m + -1m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -10m + -1m2)' equal to zero and attempt to solve:

Simplifying
13 + -10m + -1m2 = 0

Solving
13 + -10m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13 + 10m + m2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 10m + 13 + m2 = 0 + 13

Reorder the terms:
-13 + 13 + 10m + m2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 10m + m2 = 0 + 13
10m + m2 = 0 + 13

Combine like terms: 0 + 13 = 13
10m + m2 = 13

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = 13 + 25

Reorder the terms:
25 + 10m + m2 = 13 + 25

Combine like terms: 13 + 25 = 38
25 + 10m + m2 = 38

Factor a perfect square on the left side:
(m + 5)(m + 5) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(m + 5) equal to 6.164414003 and -6.164414003.


Subproblem 1
m + 5 = 6.164414003

Simplifying
m + 5 = 6.164414003

Reorder the terms:
5 + m = 6.164414003

Solving
5 + m = 6.164414003

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 6.164414003 + -5

Combine like terms: 5 + -5 = 0
0 + m = 6.164414003 + -5
m = 6.164414003 + -5

Combine like terms: 6.164414003 + -5 = 1.164414003
m = 1.164414003

Simplifying
m = 1.164414003


Subproblem 2
m + 5 = -6.164414003

Simplifying
m + 5 = -6.164414003

Reorder the terms:
5 + m = -6.164414003

Solving
5 + m = -6.164414003

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -6.164414003 + -5

Combine like terms: 5 + -5 = 0
0 + m = -6.164414003 + -5
m = -6.164414003 + -5

Combine like terms: -6.164414003 + -5 = -11.164414003
m = -11.164414003

Simplifying
m = -11.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.164414003, -11.164414003}
Solution
m = {1.164414003, -11.164414003}

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