r^2+19r-42=0

Solution for r^2+19r-42=0 equation:

Simplifying
r2 + 19r + -42 = 0

Reorder the terms:
-42 + 19r + r2 = 0

Solving
-42 + 19r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-21 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-21 + -1r)' equal to zero and attempt to solve:

Simplifying
-21 + -1r = 0

Solving
-21 + -1r = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1r = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1r = 0 + 21
-1r = 0 + 21

Combine like terms: 0 + 21 = 21
-1r = 21

Divide each side by '-1'.
r = -21

Simplifying
r = -21
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 = {-21, 2}