0=7r+r^2-170

Solution for 0=7r+r^2-170 equation:

Simplifying
0 = 7r + r2 + -170

Reorder the terms:
0 = -170 + 7r + r2

Solving
0 = -170 + 7r + r2

Solving for variable 'r'.

Combine like terms: 0 + 170 = 170
170 + -7r + -1r2 = -170 + 7r + r2 + 170 + -7r + -1r2

Reorder the terms:
170 + -7r + -1r2 = -170 + 170 + 7r + -7r + r2 + -1r2

Combine like terms: -170 + 170 = 0
170 + -7r + -1r2 = 0 + 7r + -7r + r2 + -1r2
170 + -7r + -1r2 = 7r + -7r + r2 + -1r2

Combine like terms: 7r + -7r = 0
170 + -7r + -1r2 = 0 + r2 + -1r2
170 + -7r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
170 + -7r + -1r2 = 0

Factor a trinomial.
(10 + -1r)(17 + r) = 0

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 '(17 + r)' equal to zero and attempt to solve:

Simplifying
17 + r = 0

Solving
17 + r = 0

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

Add '-17' to each side of the equation.
17 + -17 + r = 0 + -17

Combine like terms: 17 + -17 = 0
0 + r = 0 + -17
r = 0 + -17

Combine like terms: 0 + -17 = -17
r = -17

Simplifying
r = -17
Solution
r = {10, -17}