3r^2+8r-28=0

Solution for 3r^2+8r-28=0 equation:

Simplifying
3r2 + 8r + -28 = 0

Reorder the terms:
-28 + 8r + 3r2 = 0

Solving
-28 + 8r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-14 + -3r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-14 + -3r)' equal to zero and attempt to solve:

Simplifying
-14 + -3r = 0

Solving
-14 + -3r = 0

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

Add '14' to each side of the equation.
-14 + 14 + -3r = 0 + 14

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

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

Divide each side by '-3'.
r = -4.666666667

Simplifying
r = -4.666666667
Subproblem 2
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
Solution
r = {-4.666666667, 2}