14r^2+68r+48=0

Solution for 14r^2+68r+48=0 equation:

Simplifying
14r2 + 68r + 48 = 0

Reorder the terms:
48 + 68r + 14r2 = 0

Solving
48 + 68r + 14r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 34r + 7r2) = 0

Factor a trinomial.
2((4 + r)(6 + 7r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(6 + 7r)' equal to zero and attempt to solve:

Simplifying
6 + 7r = 0

Solving
6 + 7r = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7r = 0 + -6
7r = 0 + -6

Combine like terms: 0 + -6 = -6
7r = -6

Divide each side by '7'.
r = -0.8571428571

Simplifying
r = -0.8571428571
Solution
r = {-4, -0.8571428571}