15r^2+141r-90=0

Solution for 15r^2+141r-90=0 equation:

Simplifying
15r2 + 141r + -90 = 0

Reorder the terms:
-90 + 141r + 15r2 = 0

Solving
-90 + 141r + 15r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 47r + 5r2) = 0

Factor a trinomial.
3((-10 + -1r)(3 + -5r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 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 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 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 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
Solution
r = {-10, 0.6}