10r^2+41r-18=0

Solution for 10r^2+41r-18=0 equation:

Simplifying
10r2 + 41r + -18 = 0

Reorder the terms:
-18 + 41r + 10r2 = 0

Solving
-18 + 41r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -2r)(2 + -5r) = 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 '(2 + -5r)' equal to zero and attempt to solve:

Simplifying
2 + -5r = 0

Solving
2 + -5r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
Solution
r = {-4.5, 0.4}