4m^2+6m=10

Solution for 4m^2+6m=10 equation:

Simplifying
4m2 + 6m = 10

Reorder the terms:
6m + 4m2 = 10

Solving
6m + 4m2 = 10

Solving for variable 'm'.

Reorder the terms:
-10 + 6m + 4m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6m + 4m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3m + 2m2) = 0

Factor a trinomial.
2((-5 + -2m)(1 + -1m)) = 0

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

Simplifying
-5 + -2m = 0

Solving
-5 + -2m = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2m = 0 + 5
-2m = 0 + 5

Combine like terms: 0 + 5 = 5
-2m = 5

Divide each side by '-2'.
m = -2.5

Simplifying
m = -2.5
Subproblem 2
Set the factor '(1 + -1m)' equal to zero and attempt to solve:

Simplifying
1 + -1m = 0

Solving
1 + -1m = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1m = 0 + -1
-1m = 0 + -1

Combine like terms: 0 + -1 = -1
-1m = -1

Divide each side by '-1'.
m = 1

Simplifying
m = 1
Solution
m = {-2.5, 1}