-3r^2+5r+14=6

Solution for -3r^2+5r+14=6 equation:

Simplifying
-3r2 + 5r + 14 = 6

Reorder the terms:
14 + 5r + -3r2 = 6

Solving
14 + 5r + -3r2 = 6

Solving for variable 'r'.

Reorder the terms:
14 + -6 + 5r + -3r2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + 5r + -3r2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + 5r + -3r2 = 0

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

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

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

Simplifying
r = -1
Solution
r = {2.666666667, -1}