18r^2+3=-15r

Solution for 18r^2+3=-15r equation:

Simplifying
18r2 + 3 = -15r

Reorder the terms:
3 + 18r2 = -15r

Solving
3 + 18r2 = -15r

Solving for variable 'r'.

Reorder the terms:
3 + 15r + 18r2 = -15r + 15r

Combine like terms: -15r + 15r = 0
3 + 15r + 18r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 5r + 6r2) = 0

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

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

Simplifying
1 + 2r = 0

Solving
1 + 2r = 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 + 2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2r = 0 + -1
2r = 0 + -1

Combine like terms: 0 + -1 = -1
2r = -1

Divide each side by '2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {-0.5, -0.3333333333}