r^2=-42-13r

Solution for r^2=-42-13r equation:

Simplifying
r2 = -42 + -13r

Solving
r2 = -42 + -13r

Solving for variable 'r'.

Reorder the terms:
42 + 13r + r2 = -42 + -13r + 42 + 13r

Reorder the terms:
42 + 13r + r2 = -42 + 42 + -13r + 13r

Combine like terms: -42 + 42 = 0
42 + 13r + r2 = 0 + -13r + 13r
42 + 13r + r2 = -13r + 13r

Combine like terms: -13r + 13r = 0
42 + 13r + r2 = 0

Factor a trinomial.
(7 + r)(6 + 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 '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {-7, -6}