6r+3=-3r^2

Solution for 6r+3=-3r^2 equation:

Simplifying
6r + 3 = -3r2

Reorder the terms:
3 + 6r = -3r2

Solving
3 + 6r = -3r2

Solving for variable 'r'.

Combine like terms: -3r2 + 3r2 = 0
3 + 6r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 2r + r2) = 0

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