7r^2-55r+42=0

Solution for 7r^2-55r+42=0 equation:

Simplifying
7r2 + -55r + 42 = 0

Reorder the terms:
42 + -55r + 7r2 = 0

Solving
42 + -55r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + -7r)(7 + -1r) = 0

Subproblem 1
Set the factor '(6 + -7r)' equal to zero and attempt to solve:

Simplifying
6 + -7r = 0

Solving
6 + -7r = 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 + -7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7r = 0 + -6
-7r = 0 + -6

Combine like terms: 0 + -6 = -6
-7r = -6

Divide each side by '-7'.
r = 0.8571428571

Simplifying
r = 0.8571428571
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 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 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0.8571428571, 7}