r^2+18r-36=-3r^2

Solution for r^2+18r-36=-3r^2 equation:

Simplifying
r2 + 18r + -36 = -3r2

Reorder the terms:
-36 + 18r + r2 = -3r2

Solving
-36 + 18r + r2 = -3r2

Solving for variable 'r'.

Combine like terms: r2 + 3r2 = 4r2
-36 + 18r + 4r2 = -3r2 + 3r2

Combine like terms: -3r2 + 3r2 = 0
-36 + 18r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9r + 2r2) = 0

Factor a trinomial.
2((-6 + -1r)(3 + -2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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 = {-6, 1.5}