r^4+r^3=12r^2

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Solution for r^4+r^3=12r^2 equation: 


Simplifying
r4 + r3 = 12r2

Reorder the terms:
r3 + r4 = 12r2

Solving
r3 + r4 = 12r2

Solving for variable 'r'.

Reorder the terms:
-12r2 + r3 + r4 = 12r2 + -12r2

Combine like terms: 12r2 + -12r2 = 0
-12r2 + r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-12 + r + r2) = 0

Factor a trinomial.
r2((-4 + -1r)(3 + -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 '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4

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

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0, -4, 3}

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