64r^2-128r-57=0

Solution for 64r^2-128r-57=0 equation:

Simplifying
64r2 + -128r + -57 = 0

Reorder the terms:
-57 + -128r + 64r2 = 0

Solving
-57 + -128r + 64r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -8r)(19 + -8r) = 0

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

Simplifying
-3 + -8r = 0

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

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

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

Divide each side by '-8'.
r = -0.375

Simplifying
r = -0.375
Subproblem 2
Set the factor '(19 + -8r)' equal to zero and attempt to solve:

Simplifying
19 + -8r = 0

Solving
19 + -8r = 0

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

Add '-19' to each side of the equation.
19 + -19 + -8r = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -8r = 0 + -19
-8r = 0 + -19

Combine like terms: 0 + -19 = -19
-8r = -19

Divide each side by '-8'.
r = 2.375

Simplifying
r = 2.375
Solution
r = {-0.375, 2.375}