2r^2(r^2+5r+4)=0

Solution for 2r^2(r^2+5r+4)=0 equation:

Simplifying
2r2(r2 + 5r + 4) = 0

Reorder the terms:
2r2(4 + 5r + r2) = 0
(4 * 2r2 + 5r * 2r2 + r2 * 2r2) = 0
(8r2 + 10r3 + 2r4) = 0

Solving
8r2 + 10r3 + 2r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r2'.
2r2(4 + 5r + r2) = 0

Factor a trinomial.
2r2((4 + r)(1 + r)) = 0

Ignore the factor 2.
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 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 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 + r = 0 + -4

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

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

Simplifying
r = -4
Subproblem 3
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

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

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

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

Simplifying
r = -1
Solution
r = {0, -4, -1}