r^2+7r+5r+35=0

Solution for r^2+7r+5r+35=0 equation:

Simplifying
r2 + 7r + 5r + 35 = 0

Reorder the terms:
35 + 7r + 5r + r2 = 0

Combine like terms: 7r + 5r = 12r
35 + 12r + r2 = 0

Solving
35 + 12r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(7 + r)(5 + r) = 0

Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve:

Simplifying
7 + r = 0

Solving
7 + r = 0

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

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + r = 0 + -7
r = 0 + -7

Combine like terms: 0 + -7 = -7
r = -7

Simplifying
r = -7
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 0

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

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

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

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

Simplifying
r = -5
Solution
r = {-7, -5}