40r^2-64r-32=0

Solution for 40r^2-64r-32=0 equation:

Simplifying
40r2 + -64r + -32 = 0

Reorder the terms:
-32 + -64r + 40r2 = 0

Solving
-32 + -64r + 40r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -8r + 5r2) = 0

Factor a trinomial.
8((-2 + -5r)(2 + -1r)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-2 + -5r)' equal to zero and attempt to solve:

Simplifying
-2 + -5r = 0

Solving
-2 + -5r = 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 + -5r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5r = 0 + 2
-5r = 0 + 2

Combine like terms: 0 + 2 = 2
-5r = 2

Divide each side by '-5'.
r = -0.4

Simplifying
r = -0.4
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 = {-0.4, 2}