m^4-7m^2+12=0

Solution for m^4-7m^2+12=0 equation:

Simplifying
m4 + -7m2 + 12 = 0

Reorder the terms:
12 + -7m2 + m4 = 0

Solving
12 + -7m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(3 + -1m2)(4 + -1m2) = 0

Factor a difference between two squares.
(3 + -1m2)((2 + m)(2 + -1m)) = 0

Subproblem 1
Set the factor '(3 + -1m2)' equal to zero and attempt to solve:

Simplifying
3 + -1m2 = 0

Solving
3 + -1m2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m2 = 0 + -3

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

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

Divide each side by '-1'.
m2 = 3

Simplifying
m2 = 3

Take the square root of each side:
m = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

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

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

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

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

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-1.732050808, 1.732050808, -2, 2}