2r^2-9r+16=6

Solution for 2r^2-9r+16=6 equation:

Simplifying
2r2 + -9r + 16 = 6

Reorder the terms:
16 + -9r + 2r2 = 6

Solving
16 + -9r + 2r2 = 6

Solving for variable 'r'.

Reorder the terms:
16 + -6 + -9r + 2r2 = 6 + -6

Combine like terms: 16 + -6 = 10
10 + -9r + 2r2 = 6 + -6

Combine like terms: 6 + -6 = 0
10 + -9r + 2r2 = 0

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

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

Simplifying
5 + -2r = 0

Solving
5 + -2r = 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 + -2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {2, 2.5}