2r^2+9r-32=-6

Solution for 2r^2+9r-32=-6 equation:

Simplifying
2r2 + 9r + -32 = -6

Reorder the terms:
-32 + 9r + 2r2 = -6

Solving
-32 + 9r + 2r2 = -6

Solving for variable 'r'.

Reorder the terms:
-32 + 6 + 9r + 2r2 = -6 + 6

Combine like terms: -32 + 6 = -26
-26 + 9r + 2r2 = -6 + 6

Combine like terms: -6 + 6 = 0
-26 + 9r + 2r2 = 0

Factor a trinomial.
(-13 + -2r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-13 + -2r)' equal to zero and attempt to solve:

Simplifying
-13 + -2r = 0

Solving
-13 + -2r = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2r = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2r = 0 + 13
-2r = 0 + 13

Combine like terms: 0 + 13 = 13
-2r = 13

Divide each side by '-2'.
r = -6.5

Simplifying
r = -6.5
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-6.5, 2}