12r^2+29r-8=0

Solution for 12r^2+29r-8=0 equation:

Simplifying
12r2 + 29r + -8 = 0

Reorder the terms:
-8 + 29r + 12r2 = 0

Solving
-8 + 29r + 12r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + -3r)(1 + -4r) = 0

Subproblem 1
Set the factor '(-8 + -3r)' equal to zero and attempt to solve:

Simplifying
-8 + -3r = 0

Solving
-8 + -3r = 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 + -3r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3r = 0 + 8
-3r = 0 + 8

Combine like terms: 0 + 8 = 8
-3r = 8

Divide each side by '-3'.
r = -2.666666667

Simplifying
r = -2.666666667
Subproblem 2
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Solution
r = {-2.666666667, 0.25}