3m^2+1=-4m

Solution for 3m^2+1=-4m equation:

Simplifying
3m2 + 1 = -4m

Reorder the terms:
1 + 3m2 = -4m

Solving
1 + 3m2 = -4m

Solving for variable 'm'.

Reorder the terms:
1 + 4m + 3m2 = -4m + 4m

Combine like terms: -4m + 4m = 0
1 + 4m + 3m2 = 0

Factor a trinomial.
(1 + m)(1 + 3m) = 0

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

Simplifying
1 + m = 0

Solving
1 + m = 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 + m = 0 + -1

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

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

Simplifying
m = -1
Subproblem 2
Set the factor '(1 + 3m)' equal to zero and attempt to solve:

Simplifying
1 + 3m = 0

Solving
1 + 3m = 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 + 3m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3m = 0 + -1
3m = 0 + -1

Combine like terms: 0 + -1 = -1
3m = -1

Divide each side by '3'.
m = -0.3333333333

Simplifying
m = -0.3333333333
Solution
m = {-1, -0.3333333333}