2r^2+9=-9r

Solution for 2r^2+9=-9r equation:

Simplifying
2r2 + 9 = -9r

Reorder the terms:
9 + 2r2 = -9r

Solving
9 + 2r2 = -9r

Solving for variable 'r'.

Reorder the terms:
9 + 9r + 2r2 = -9r + 9r

Combine like terms: -9r + 9r = 0
9 + 9r + 2r2 = 0

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

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

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

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

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

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

Simplifying
3 + 2r = 0

Solving
3 + 2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2r = 0 + -3
2r = 0 + -3

Combine like terms: 0 + -3 = -3
2r = -3

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Solution
r = {-3, -1.5}