r^2(r^2-3r+10)=0

Solution for r^2(r^2-3r+10)=0 equation:

Simplifying
r2(r2 + -3r + 10) = 0

Reorder the terms:
r2(10 + -3r + r2) = 0
(10 * r2 + -3r * r2 + r2 * r2) = 0
(10r2 + -3r3 + r4) = 0

Solving
10r2 + -3r3 + r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(10 + -3r + r2) = 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 '(10 + -3r + r2)' equal to zero and attempt to solve:

Simplifying
10 + -3r + r2 = 0

Solving
10 + -3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + -3r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3r + r2 = 0 + -10
-3r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3r + r2 = -10

The r term is -3r.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3r + 2.25 + r2 = -10 + 2.25

Reorder the terms:
2.25 + -3r + r2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3r + r2 = -7.75

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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