r^2+3r-270=0

Solution for r^2+3r-270=0 equation:

Simplifying
r2 + 3r + -270 = 0

Reorder the terms:
-270 + 3r + r2 = 0

Solving
-270 + 3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-18 + -1r)(15 + -1r) = 0

Subproblem 1
Set the factor '(-18 + -1r)' equal to zero and attempt to solve:

Simplifying
-18 + -1r = 0

Solving
-18 + -1r = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1r = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1r = 0 + 18
-1r = 0 + 18

Combine like terms: 0 + 18 = 18
-1r = 18

Divide each side by '-1'.
r = -18

Simplifying
r = -18
Subproblem 2
Set the factor '(15 + -1r)' equal to zero and attempt to solve:

Simplifying
15 + -1r = 0

Solving
15 + -1r = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1r = 0 + -15
-1r = 0 + -15

Combine like terms: 0 + -15 = -15
-1r = -15

Divide each side by '-1'.
r = 15

Simplifying
r = 15
Solution
r = {-18, 15}