r^4=5r^3+14r^2

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Solution for r^4=5r^3+14r^2 equation: 


Simplifying
r4 = 5r3 + 14r2

Reorder the terms:
r4 = 14r2 + 5r3

Solving
r4 = 14r2 + 5r3

Solving for variable 'r'.

Reorder the terms:
-14r2 + -5r3 + r4 = 14r2 + 5r3 + -14r2 + -5r3

Reorder the terms:
-14r2 + -5r3 + r4 = 14r2 + -14r2 + 5r3 + -5r3

Combine like terms: 14r2 + -14r2 = 0
-14r2 + -5r3 + r4 = 0 + 5r3 + -5r3
-14r2 + -5r3 + r4 = 5r3 + -5r3

Combine like terms: 5r3 + -5r3 = 0
-14r2 + -5r3 + r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-14 + -5r + r2) = 0

Factor a trinomial.
r2((-2 + -1r)(7 + -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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0, -2, 7}

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