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

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

Simplifying
r4 + -7r2 + 12 = 0

Reorder the terms:
12 + -7r2 + r4 = 0

Solving
12 + -7r2 + r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r2)(4 + -1r2) = 0

Factor a difference between two squares.
(3 + -1r2)((2 + r)(2 + -1r)) = 0

Subproblem 1
Set the factor '(3 + -1r2)' equal to zero and attempt to solve:

Simplifying
3 + -1r2 = 0

Solving
3 + -1r2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r2 = 0 + -3
-1r2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1r2 = -3

Divide each side by '-1'.
r2 = 3

Simplifying
r2 = 3

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

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

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