36+51r^2-15r^4=

Solution for 36+51r^2-15r^4= equation:

Simplifying
36 + 51r2 + -15r4 = 0

Solving
36 + 51r2 + -15r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 17r2 + -5r4) = 0

Factor a trinomial.
3((4 + -1r2)(3 + 5r2)) = 0

Factor a difference between two squares.
3(((2 + r)(2 + -1r))(3 + 5r2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 5r2)' equal to zero and attempt to solve:

Simplifying
3 + 5r2 = 0

Solving
3 + 5r2 = 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 + 5r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5r2 = 0 + -3
5r2 = 0 + -3

Combine like terms: 0 + -3 = -3
5r2 = -3

Divide each side by '5'.
r2 = -0.6

Simplifying
r2 = -0.6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-2, 2}