55r^2+31r-42=0

Solution for 55r^2+31r-42=0 equation:

Simplifying
55r2 + 31r + -42 = 0

Reorder the terms:
-42 + 31r + 55r2 = 0

Solving
-42 + 31r + 55r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -5r)(7 + -11r) = 0

Subproblem 1
Set the factor '(-6 + -5r)' equal to zero and attempt to solve:

Simplifying
-6 + -5r = 0

Solving
-6 + -5r = 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 + -5r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5r = 0 + 6
-5r = 0 + 6

Combine like terms: 0 + 6 = 6
-5r = 6

Divide each side by '-5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
Set the factor '(7 + -11r)' equal to zero and attempt to solve:

Simplifying
7 + -11r = 0

Solving
7 + -11r = 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 + -11r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -11r = 0 + -7
-11r = 0 + -7

Combine like terms: 0 + -7 = -7
-11r = -7

Divide each side by '-11'.
r = 0.6363636364

Simplifying
r = 0.6363636364
Solution
r = {-1.2, 0.6363636364}