10m^2+3m-6=

Solution for 10m^2+3m-6= equation:

Simplifying
10m2 + 3m + -6 = 0

Reorder the terms:
-6 + 3m + 10m2 = 0

Solving
-6 + 3m + 10m2 = 0

Solving for variable 'm'.

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

Divide each side by '10'.
-0.6 + 0.3m + m2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.3m + 0.6 + m2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.3m + m2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.3m + m2 = 0 + 0.6
0.3m + m2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.3m + m2 = 0.6

The m term is 0.3m.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3m + 0.0225 + m2 = 0.6 + 0.0225

Reorder the terms:
0.0225 + 0.3m + m2 = 0.6 + 0.0225

Combine like terms: 0.6 + 0.0225 = 0.6225
0.0225 + 0.3m + m2 = 0.6225

Factor a perfect square on the left side:
(m + 0.15)(m + 0.15) = 0.6225

Calculate the square root of the right side: 0.788986692

Break this problem into two subproblems by setting 
(m + 0.15) equal to 0.788986692 and -0.788986692.

Subproblem 1
m + 0.15 = 0.788986692

Simplifying
m + 0.15 = 0.788986692

Reorder the terms:
0.15 + m = 0.788986692

Solving
0.15 + m = 0.788986692

Solving for variable 'm'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + m = 0.788986692 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + m = 0.788986692 + -0.15
m = 0.788986692 + -0.15

Combine like terms: 0.788986692 + -0.15 = 0.638986692
m = 0.638986692

Simplifying
m = 0.638986692

Subproblem 2
m + 0.15 = -0.788986692

Simplifying
m + 0.15 = -0.788986692

Reorder the terms:
0.15 + m = -0.788986692

Solving
0.15 + m = -0.788986692

Solving for variable 'm'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + m = -0.788986692 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + m = -0.788986692 + -0.15
m = -0.788986692 + -0.15

Combine like terms: -0.788986692 + -0.15 = -0.938986692
m = -0.938986692

Simplifying
m = -0.938986692

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.638986692, -0.938986692}