2r^2+24r-90=0

Solution for 2r^2+24r-90=0 equation:

Simplifying
2r2 + 24r + -90 = 0

Reorder the terms:
-90 + 24r + 2r2 = 0

Solving
-90 + 24r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 12r + r2) = 0

Factor a trinomial.
2((-15 + -1r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-15, 3}