r^2+14r-32=0

Solution for r^2+14r-32=0 equation:

Simplifying
r2 + 14r + -32 = 0

Reorder the terms:
-32 + 14r + r2 = 0

Solving
-32 + 14r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-16 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -1r)' equal to zero and attempt to solve:

Simplifying
-16 + -1r = 0

Solving
-16 + -1r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1r = 0 + 16
-1r = 0 + 16

Combine like terms: 0 + 16 = 16
-1r = 16

Divide each side by '-1'.
r = -16

Simplifying
r = -16
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 = {-16, 2}