6r^2+20r+16=0

Solution for 6r^2+20r+16=0 equation:

Simplifying
6r2 + 20r + 16 = 0

Reorder the terms:
16 + 20r + 6r2 = 0

Solving
16 + 20r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 10r + 3r2) = 0

Factor a trinomial.
2((2 + r)(4 + 3r)) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(4 + 3r)' equal to zero and attempt to solve:

Simplifying
4 + 3r = 0

Solving
4 + 3r = 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 + 3r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3r = 0 + -4
3r = 0 + -4

Combine like terms: 0 + -4 = -4
3r = -4

Divide each side by '3'.
r = -1.333333333

Simplifying
r = -1.333333333
Solution
r = {-2, -1.333333333}