3r^2-42=11r

Solution for 3r^2-42=11r equation:

Simplifying
3r2 + -42 = 11r

Reorder the terms:
-42 + 3r2 = 11r

Solving
-42 + 3r2 = 11r

Solving for variable 'r'.

Reorder the terms:
-42 + -11r + 3r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-42 + -11r + 3r2 = 0

Factor a trinomial.
(-7 + -3r)(6 + -1r) = 0

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

Simplifying
-7 + -3r = 0

Solving
-7 + -3r = 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 + -3r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3r = 0 + 7
-3r = 0 + 7

Combine like terms: 0 + 7 = 7
-3r = 7

Divide each side by '-3'.
r = -2.333333333

Simplifying
r = -2.333333333
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 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 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-2.333333333, 6}