10r^2-19r=33

Solution for 10r^2-19r=33 equation:

Simplifying
10r2 + -19r = 33

Reorder the terms:
-19r + 10r2 = 33

Solving
-19r + 10r2 = 33

Solving for variable 'r'.

Reorder the terms:
-33 + -19r + 10r2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -19r + 10r2 = 0

Factor a trinomial.
(-11 + -10r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-11 + -10r)' equal to zero and attempt to solve:

Simplifying
-11 + -10r = 0

Solving
-11 + -10r = 0

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

Add '11' to each side of the equation.
-11 + 11 + -10r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -10r = 0 + 11
-10r = 0 + 11

Combine like terms: 0 + 11 = 11
-10r = 11

Divide each side by '-10'.
r = -1.1

Simplifying
r = -1.1
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1.1, 3}