3r^1+3r^2+3=129

Solution for 3r^1+3r^2+3=129 equation:

Simplifying
3r + 3r2 + 3 = 129

Reorder the terms:
3 + 3r + 3r2 = 129

Solving
3 + 3r + 3r2 = 129

Solving for variable 'r'.

Reorder the terms:
3 + -129 + 3r + 3r2 = 129 + -129

Combine like terms: 3 + -129 = -126
-126 + 3r + 3r2 = 129 + -129

Combine like terms: 129 + -129 = 0
-126 + 3r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + r + r2) = 0

Factor a trinomial.
3((-7 + -1r)(6 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7
Subproblem 2
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
Solution
r = {-7, 6}