3r^2-14r=-16

Solution for 3r^2-14r=-16 equation:

Simplifying
3r2 + -14r = -16

Reorder the terms:
-14r + 3r2 = -16

Solving
-14r + 3r2 = -16

Solving for variable 'r'.

Reorder the terms:
16 + -14r + 3r2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -14r + 3r2 = 0

Factor a trinomial.
(2 + -1r)(8 + -3r) = 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 '(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 = {2, 2.666666667}