2r^2-105=11r

Solution for 2r^2-105=11r equation:

Simplifying
2r2 + -105 = 11r

Reorder the terms:
-105 + 2r2 = 11r

Solving
-105 + 2r2 = 11r

Solving for variable 'r'.

Reorder the terms:
-105 + -11r + 2r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-105 + -11r + 2r2 = 0

Factor a trinomial.
(-5 + -1r)(21 + -2r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(21 + -2r)' equal to zero and attempt to solve:

Simplifying
21 + -2r = 0

Solving
21 + -2r = 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 + -2r = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2r = 0 + -21
-2r = 0 + -21

Combine like terms: 0 + -21 = -21
-2r = -21

Divide each side by '-2'.
r = 10.5

Simplifying
r = 10.5
Solution
r = {-5, 10.5}