r^4=3r^3+10r^2

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Solution for r^4=3r^3+10r^2 equation: 


Simplifying
r4 = 3r3 + 10r2

Reorder the terms:
r4 = 10r2 + 3r3

Solving
r4 = 10r2 + 3r3

Solving for variable 'r'.

Reorder the terms:
-10r2 + -3r3 + r4 = 10r2 + 3r3 + -10r2 + -3r3

Reorder the terms:
-10r2 + -3r3 + r4 = 10r2 + -10r2 + 3r3 + -3r3

Combine like terms: 10r2 + -10r2 = 0
-10r2 + -3r3 + r4 = 0 + 3r3 + -3r3
-10r2 + -3r3 + r4 = 3r3 + -3r3

Combine like terms: 3r3 + -3r3 = 0
-10r2 + -3r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-10 + -3r + r2) = 0

Factor a trinomial.
r2((-2 + -1r)(5 + -1r)) = 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 + -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

Subproblem 3
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {0, -2, 5}

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