0=-42-35r-7r^2

Solution for 0=-42-35r-7r^2 equation:

Simplifying
0 = -42 + -35r + -7r2

Solving
0 = -42 + -35r + -7r2

Solving for variable 'r'.

Combine like terms: 0 + 42 = 42
42 + 35r + 7r2 = -42 + -35r + -7r2 + 42 + 35r + 7r2

Reorder the terms:
42 + 35r + 7r2 = -42 + 42 + -35r + 35r + -7r2 + 7r2

Combine like terms: -42 + 42 = 0
42 + 35r + 7r2 = 0 + -35r + 35r + -7r2 + 7r2
42 + 35r + 7r2 = -35r + 35r + -7r2 + 7r2

Combine like terms: -35r + 35r = 0
42 + 35r + 7r2 = 0 + -7r2 + 7r2
42 + 35r + 7r2 = -7r2 + 7r2

Combine like terms: -7r2 + 7r2 = 0
42 + 35r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + 5r + r2) = 0

Factor a trinomial.
7((3 + r)(2 + r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

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

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

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

Simplifying
r = -2
Solution
r = {-3, -2}