5r^2+45r+90=0

Solution for 5r^2+45r+90=0 equation:

Simplifying
5r2 + 45r + 90 = 0

Reorder the terms:
90 + 45r + 5r2 = 0

Solving
90 + 45r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + 9r + r2) = 0

Factor a trinomial.
5((6 + r)(3 + r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

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

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

Simplifying
r = -3
Solution
r = {-6, -3}