10r^2+17r-32=-5

Solution for 10r^2+17r-32=-5 equation:

Simplifying
10r2 + 17r + -32 = -5

Reorder the terms:
-32 + 17r + 10r2 = -5

Solving
-32 + 17r + 10r2 = -5

Solving for variable 'r'.

Reorder the terms:
-32 + 5 + 17r + 10r2 = -5 + 5

Combine like terms: -32 + 5 = -27
-27 + 17r + 10r2 = -5 + 5

Combine like terms: -5 + 5 = 0
-27 + 17r + 10r2 = 0

Factor a trinomial.
(-27 + -10r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-27 + -10r)' equal to zero and attempt to solve:

Simplifying
-27 + -10r = 0

Solving
-27 + -10r = 0

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

Add '27' to each side of the equation.
-27 + 27 + -10r = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -10r = 0 + 27
-10r = 0 + 27

Combine like terms: 0 + 27 = 27
-10r = 27

Divide each side by '-10'.
r = -2.7

Simplifying
r = -2.7
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-2.7, 1}