7r^2-8r-12=0

Solution for 7r^2-8r-12=0 equation:

Simplifying
7r2 + -8r + -12 = 0

Reorder the terms:
-12 + -8r + 7r2 = 0

Solving
-12 + -8r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -7r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-6 + -7r)' equal to zero and attempt to solve:

Simplifying
-6 + -7r = 0

Solving
-6 + -7r = 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 + -7r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7r = 0 + 6
-7r = 0 + 6

Combine like terms: 0 + 6 = 6
-7r = 6

Divide each side by '-7'.
r = -0.8571428571

Simplifying
r = -0.8571428571
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-0.8571428571, 2}