-4r^2=18r+18

Solution for -4r^2=18r+18 equation:

Simplifying
-4r2 = 18r + 18

Reorder the terms:
-4r2 = 18 + 18r

Solving
-4r2 = 18 + 18r

Solving for variable 'r'.

Reorder the terms:
-18 + -18r + -4r2 = 18 + 18r + -18 + -18r

Reorder the terms:
-18 + -18r + -4r2 = 18 + -18 + 18r + -18r

Combine like terms: 18 + -18 = 0
-18 + -18r + -4r2 = 0 + 18r + -18r
-18 + -18r + -4r2 = 18r + -18r

Combine like terms: 18r + -18r = 0
-18 + -18r + -4r2 = 0

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

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

Ignore the factor -2.
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}