77r^2+23r-12=0

Solution for 77r^2+23r-12=0 equation:

Simplifying
77r2 + 23r + -12 = 0

Reorder the terms:
-12 + 23r + 77r2 = 0

Solving
-12 + 23r + 77r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -7r)(3 + -11r) = 0

Subproblem 1
Set the factor '(-4 + -7r)' equal to zero and attempt to solve:

Simplifying
-4 + -7r = 0

Solving
-4 + -7r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7r = 0 + 4
-7r = 0 + 4

Combine like terms: 0 + 4 = 4
-7r = 4

Divide each side by '-7'.
r = -0.5714285714

Simplifying
r = -0.5714285714
Subproblem 2
Set the factor '(3 + -11r)' equal to zero and attempt to solve:

Simplifying
3 + -11r = 0

Solving
3 + -11r = 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 + -11r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -11r = 0 + -3
-11r = 0 + -3

Combine like terms: 0 + -3 = -3
-11r = -3

Divide each side by '-11'.
r = 0.2727272727

Simplifying
r = 0.2727272727
Solution
r = {-0.5714285714, 0.2727272727}