6r^2+47r+90=0

Solution for 6r^2+47r+90=0 equation:

Simplifying
6r2 + 47r + 90 = 0

Reorder the terms:
90 + 47r + 6r2 = 0

Solving
90 + 47r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(9 + 2r)(10 + 3r) = 0

Subproblem 1
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Subproblem 2
Set the factor '(10 + 3r)' equal to zero and attempt to solve:

Simplifying
10 + 3r = 0

Solving
10 + 3r = 0

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

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

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

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

Divide each side by '3'.
r = -3.333333333

Simplifying
r = -3.333333333
Solution
r = {-4.5, -3.333333333}