r^4=3r^3+40r^2

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Solution for r^4=3r^3+40r^2 equation: 


Simplifying
r4 = 3r3 + 40r2

Reorder the terms:
r4 = 40r2 + 3r3

Solving
r4 = 40r2 + 3r3

Solving for variable 'r'.

Reorder the terms:
-40r2 + -3r3 + r4 = 40r2 + 3r3 + -40r2 + -3r3

Reorder the terms:
-40r2 + -3r3 + r4 = 40r2 + -40r2 + 3r3 + -3r3

Combine like terms: 40r2 + -40r2 = 0
-40r2 + -3r3 + r4 = 0 + 3r3 + -3r3
-40r2 + -3r3 + r4 = 3r3 + -3r3

Combine like terms: 3r3 + -3r3 = 0
-40r2 + -3r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-40 + -3r + r2) = 0

Factor a trinomial.
r2((-5 + -1r)(8 + -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 '(-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

Subproblem 3
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {0, -5, 8}

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