R^4-3r^2+2=0

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Solution for R^4-3r^2+2=0 equation: 


Simplifying
R4 + -3r2 + 2 = 0

Reorder the terms:
2 + R4 + -3r2 = 0

Solving
2 + R4 + -3r2 = 0

Solving for variable 'R'.

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

Add '-2' to each side of the equation.
2 + R4 + -2 + -3r2 = 0 + -2

Reorder the terms:
2 + -2 + R4 + -3r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + R4 + -3r2 = 0 + -2
R4 + -3r2 = 0 + -2

Combine like terms: 0 + -2 = -2
R4 + -3r2 = -2

Add '3r2' to each side of the equation.
R4 + -3r2 + 3r2 = -2 + 3r2

Combine like terms: -3r2 + 3r2 = 0
R4 + 0 = -2 + 3r2
R4 = -2 + 3r2

Simplifying
R4 = -2 + 3r2

Reorder the terms:
2 + R4 + -3r2 = -2 + 3r2 + 2 + -3r2

Reorder the terms:
2 + R4 + -3r2 = -2 + 2 + 3r2 + -3r2

Combine like terms: -2 + 2 = 0
2 + R4 + -3r2 = 0 + 3r2 + -3r2
2 + R4 + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
2 + R4 + -3r2 = 0

Factor a trinomial.
(R2 + -1r)(R2 + 3r) = 0


Subproblem 1
Set the factor '(R2 + -1r)' equal to zero and attempt to solve:

Simplifying
R2 + -1r = 0

Solving
R2 + -1r = 0

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

Add 'r' to each side of the equation.
R2 + -1r + r = 0 + r

Combine like terms: -1r + r = 0
R2 + 0 = 0 + r
R2 = 0 + r
Remove the zero:
R2 = r

Simplifying
R2 = r

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 '(R2 + 3r)' equal to zero and attempt to solve:

Simplifying
R2 + 3r = 0

Solving
R2 + 3r = 0

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

Add '-3r' to each side of the equation.
R2 + 3r + -3r = 0 + -3r

Combine like terms: 3r + -3r = 0
R2 + 0 = 0 + -3r
R2 = 0 + -3r
Remove the zero:
R2 = -3r

Simplifying
R2 = -3r

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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