3=13r-14r^2

Solution for 3=13r-14r^2 equation:

Simplifying
3 = 13r + -14r2

Solving
3 = 13r + -14r2

Solving for variable 'r'.

Reorder the terms:
3 + -13r + 14r2 = 13r + -13r + -14r2 + 14r2

Combine like terms: 13r + -13r = 0
3 + -13r + 14r2 = 0 + -14r2 + 14r2
3 + -13r + 14r2 = -14r2 + 14r2

Combine like terms: -14r2 + 14r2 = 0
3 + -13r + 14r2 = 0

Factor a trinomial.
(3 + -7r)(1 + -2r) = 0

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

Simplifying
3 + -7r = 0

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

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

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

Divide each side by '-7'.
r = 0.4285714286

Simplifying
r = 0.4285714286
Subproblem 2
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
Solution
r = {0.4285714286, 0.5}