-4r^4+5r^2+6=0

Solution for -4r^4+5r^2+6=0 equation:

Simplifying
-4r4 + 5r2 + 6 = 0

Reorder the terms:
6 + 5r2 + -4r4 = 0

Solving
6 + 5r2 + -4r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -1r2)(3 + 4r2) = 0

Subproblem 1
Set the factor '(2 + -1r2)' equal to zero and attempt to solve:

Simplifying
2 + -1r2 = 0

Solving
2 + -1r2 = 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 + -1r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r2 = 0 + -2
-1r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1r2 = -2

Divide each side by '-1'.
r2 = 2

Simplifying
r2 = 2

Take the square root of each side:
r = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + 4r2)' equal to zero and attempt to solve:

Simplifying
3 + 4r2 = 0

Solving
3 + 4r2 = 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 + 4r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r2 = 0 + -3
4r2 = 0 + -3

Combine like terms: 0 + -3 = -3
4r2 = -3

Divide each side by '4'.
r2 = -0.75

Simplifying
r2 = -0.75

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {-1.414213562, 1.414213562}