4r^2=r^6

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Solution for 4r^2=r^6 equation: 


Simplifying
4r2 = r6

Solving
4r2 = r6

Solving for variable 'r'.

Combine like terms: r6 + -1r6 = 0
4r2 + -1r6 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(4 + -1r4) = 0

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


Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}

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

Simplifying
2 + r2 = 0

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

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

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

Simplifying
r2 = -2

The solution to this equation could not be determined.

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

Subproblem 3
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}
Solution
r = {0, -1.414213562, 1.414213562}

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