r^2+2r+5r+10=0

Solution for r^2+2r+5r+10=0 equation:

Simplifying
r2 + 2r + 5r + 10 = 0

Reorder the terms:
10 + 2r + 5r + r2 = 0

Combine like terms: 2r + 5r = 7r
10 + 7r + r2 = 0

Solving
10 + 7r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + r)(2 + r) = 0

Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

Simplifying
r = -2
Solution
r = {-5, -2}