16r^2+27r+6=-5r^2

Solution for 16r^2+27r+6=-5r^2 equation:

Simplifying
16r2 + 27r + 6 = -5r2

Reorder the terms:
6 + 27r + 16r2 = -5r2

Solving
6 + 27r + 16r2 = -5r2

Solving for variable 'r'.

Combine like terms: 16r2 + 5r2 = 21r2
6 + 27r + 21r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
6 + 27r + 21r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 9r + 7r2) = 0

Factor a trinomial.
3((1 + r)(2 + 7r)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + 7r)' equal to zero and attempt to solve:

Simplifying
2 + 7r = 0

Solving
2 + 7r = 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 + 7r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7r = 0 + -2
7r = 0 + -2

Combine like terms: 0 + -2 = -2
7r = -2

Divide each side by '7'.
r = -0.2857142857

Simplifying
r = -0.2857142857
Solution
r = {-1, -0.2857142857}