-8m^2+4m+10=0

Solution for -8m^2+4m+10=0 equation:

Simplifying
-8m2 + 4m + 10 = 0

Reorder the terms:
10 + 4m + -8m2 = 0

Solving
10 + 4m + -8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 2m + -4m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 2m + -4m2)' equal to zero and attempt to solve:

Simplifying
5 + 2m + -4m2 = 0

Solving
5 + 2m + -4m2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -0.5m + m2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.5m + 1.25 + m2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.5m + m2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.5m + m2 = 0 + 1.25
-0.5m + m2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.5m + m2 = 1.25

The m term is -0.5m.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5m + 0.0625 + m2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + -0.5m + m2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + -0.5m + m2 = 1.3125

Factor a perfect square on the left side:
(m + -0.25)(m + -0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(m + -0.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
m + -0.25 = 1.145643924

Simplifying
m + -0.25 = 1.145643924

Reorder the terms:
-0.25 + m = 1.145643924

Solving
-0.25 + m = 1.145643924

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = 1.145643924 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = 1.145643924 + 0.25
m = 1.145643924 + 0.25

Combine like terms: 1.145643924 + 0.25 = 1.395643924
m = 1.395643924

Simplifying
m = 1.395643924

Subproblem 2
m + -0.25 = -1.145643924

Simplifying
m + -0.25 = -1.145643924

Reorder the terms:
-0.25 + m = -1.145643924

Solving
-0.25 + m = -1.145643924

Solving for variable 'm'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + m = -1.145643924 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + m = -1.145643924 + 0.25
m = -1.145643924 + 0.25

Combine like terms: -1.145643924 + 0.25 = -0.895643924
m = -0.895643924

Simplifying
m = -0.895643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.395643924, -0.895643924}
Solution
m = {1.395643924, -0.895643924}