(-13r^4+3r^2+12r^5)+(7r^4+6r^2)=0

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Solution for (-13r^4+3r^2+12r^5)+(7r^4+6r^2)=0 equation: 


Simplifying
(-13r4 + 3r2 + 12r5) + (7r4 + 6r2) = 0

Reorder the terms:
(3r2 + -13r4 + 12r5) + (7r4 + 6r2) = 0

Remove parenthesis around (3r2 + -13r4 + 12r5)
3r2 + -13r4 + 12r5 + (7r4 + 6r2) = 0

Reorder the terms:
3r2 + -13r4 + 12r5 + (6r2 + 7r4) = 0

Remove parenthesis around (6r2 + 7r4)
3r2 + -13r4 + 12r5 + 6r2 + 7r4 = 0

Reorder the terms:
3r2 + 6r2 + -13r4 + 7r4 + 12r5 = 0

Combine like terms: 3r2 + 6r2 = 9r2
9r2 + -13r4 + 7r4 + 12r5 = 0

Combine like terms: -13r4 + 7r4 = -6r4
9r2 + -6r4 + 12r5 = 0

Solving
9r2 + -6r4 + 12r5 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r2'.
3r2(3 + -2r2 + 4r3) = 0

Ignore the factor 3.

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 '(3 + -2r2 + 4r3)' equal to zero and attempt to solve:

Simplifying
3 + -2r2 + 4r3 = 0

Solving
3 + -2r2 + 4r3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}

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