15m^2+18m-21=

Solution for 15m^2+18m-21= equation:

Simplifying
15m2 + 18m + -21 = 0

Reorder the terms:
-21 + 18m + 15m2 = 0

Solving
-21 + 18m + 15m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 6m + 5m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 6m + 5m2)' equal to zero and attempt to solve:

Simplifying
-7 + 6m + 5m2 = 0

Solving
-7 + 6m + 5m2 = 0

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

Divide each side by '5'.
-1.4 + 1.2m + m2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 1.2m + 1.4 + m2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 1.2m + m2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 1.2m + m2 = 0 + 1.4
1.2m + m2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
1.2m + m2 = 1.4

The m term is 1.2m.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2m + 0.36 + m2 = 1.4 + 0.36

Reorder the terms:
0.36 + 1.2m + m2 = 1.4 + 0.36

Combine like terms: 1.4 + 0.36 = 1.76
0.36 + 1.2m + m2 = 1.76

Factor a perfect square on the left side:
(m + 0.6)(m + 0.6) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(m + 0.6) equal to 1.326649916 and -1.326649916.

Subproblem 1
m + 0.6 = 1.326649916

Simplifying
m + 0.6 = 1.326649916

Reorder the terms:
0.6 + m = 1.326649916

Solving
0.6 + m = 1.326649916

Solving for variable 'm'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + m = 1.326649916 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + m = 1.326649916 + -0.6
m = 1.326649916 + -0.6

Combine like terms: 1.326649916 + -0.6 = 0.726649916
m = 0.726649916

Simplifying
m = 0.726649916

Subproblem 2
m + 0.6 = -1.326649916

Simplifying
m + 0.6 = -1.326649916

Reorder the terms:
0.6 + m = -1.326649916

Solving
0.6 + m = -1.326649916

Solving for variable 'm'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + m = -1.326649916 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + m = -1.326649916 + -0.6
m = -1.326649916 + -0.6

Combine like terms: -1.326649916 + -0.6 = -1.926649916
m = -1.926649916

Simplifying
m = -1.926649916

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.726649916, -1.926649916}
Solution
m = {0.726649916, -1.926649916}