16=38r+-12r^2

Solution for 16=38r+-12r^2 equation:

Simplifying
16 = 38r + -12r2

Solving
16 = 38r + -12r2

Solving for variable 'r'.

Reorder the terms:
16 + -38r + 12r2 = 38r + -38r + -12r2 + 12r2

Combine like terms: 38r + -38r = 0
16 + -38r + 12r2 = 0 + -12r2 + 12r2
16 + -38r + 12r2 = -12r2 + 12r2

Combine like terms: -12r2 + 12r2 = 0
16 + -38r + 12r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -19r + 6r2) = 0

Factor a trinomial.
2((1 + -2r)(8 + -3r)) = 0

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

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

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(8 + -3r)' equal to zero and attempt to solve:

Simplifying
8 + -3r = 0

Solving
8 + -3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3r = 0 + -8
-3r = 0 + -8

Combine like terms: 0 + -8 = -8
-3r = -8

Divide each side by '-3'.
r = 2.666666667

Simplifying
r = 2.666666667
Solution
r = {0.5, 2.666666667}