56r^2-8r-48=0

Solution for 56r^2-8r-48=0 equation:

Simplifying
56r2 + -8r + -48 = 0

Reorder the terms:
-48 + -8r + 56r2 = 0

Solving
-48 + -8r + 56r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + -1r + 7r2) = 0

Factor a trinomial.
8((-6 + -7r)(1 + -1r)) = 0

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

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

Simplifying
r = 1
Solution
r = {-0.8571428571, 1}