40r^2=192+208r

Solution for 40r^2=192+208r equation:

Simplifying
40r2 = 192 + 208r

Solving
40r2 = 192 + 208r

Solving for variable 'r'.

Reorder the terms:
-192 + -208r + 40r2 = 192 + 208r + -192 + -208r

Reorder the terms:
-192 + -208r + 40r2 = 192 + -192 + 208r + -208r

Combine like terms: 192 + -192 = 0
-192 + -208r + 40r2 = 0 + 208r + -208r
-192 + -208r + 40r2 = 208r + -208r

Combine like terms: 208r + -208r = 0
-192 + -208r + 40r2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-24 + -26r + 5r2) = 0

Factor a trinomial.
8((-4 + -5r)(6 + -1r)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve:

Simplifying
-4 + -5r = 0

Solving
-4 + -5r = 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 + -5r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5r = 0 + 4
-5r = 0 + 4

Combine like terms: 0 + 4 = 4
-5r = 4

Divide each side by '-5'.
r = -0.8

Simplifying
r = -0.8
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 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 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-0.8, 6}