3r^2+9r-163=-r^2-3-3r

Solution for 3r^2+9r-163=-r^2-3-3r equation:

Simplifying
3r2 + 9r + -163 = -1r2 + -3 + -3r

Reorder the terms:
-163 + 9r + 3r2 = -1r2 + -3 + -3r

Reorder the terms:
-163 + 9r + 3r2 = -3 + -3r + -1r2

Solving
-163 + 9r + 3r2 = -3 + -3r + -1r2

Solving for variable 'r'.

Reorder the terms:
-163 + 3 + 9r + 3r + 3r2 + r2 = -3 + -3r + -1r2 + 3 + 3r + r2

Combine like terms: -163 + 3 = -160
-160 + 9r + 3r + 3r2 + r2 = -3 + -3r + -1r2 + 3 + 3r + r2

Combine like terms: 9r + 3r = 12r
-160 + 12r + 3r2 + r2 = -3 + -3r + -1r2 + 3 + 3r + r2

Combine like terms: 3r2 + r2 = 4r2
-160 + 12r + 4r2 = -3 + -3r + -1r2 + 3 + 3r + r2

Reorder the terms:
-160 + 12r + 4r2 = -3 + 3 + -3r + 3r + -1r2 + r2

Combine like terms: -3 + 3 = 0
-160 + 12r + 4r2 = 0 + -3r + 3r + -1r2 + r2
-160 + 12r + 4r2 = -3r + 3r + -1r2 + r2

Combine like terms: -3r + 3r = 0
-160 + 12r + 4r2 = 0 + -1r2 + r2
-160 + 12r + 4r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
-160 + 12r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 3r + r2) = 0

Factor a trinomial.
4((-8 + -1r)(5 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-8, 5}