8r^2=24-16r

Solution for 8r^2=24-16r equation:

Simplifying
8r2 = 24 + -16r

Solving
8r2 = 24 + -16r

Solving for variable 'r'.

Reorder the terms:
-24 + 16r + 8r2 = 24 + -16r + -24 + 16r

Reorder the terms:
-24 + 16r + 8r2 = 24 + -24 + -16r + 16r

Combine like terms: 24 + -24 = 0
-24 + 16r + 8r2 = 0 + -16r + 16r
-24 + 16r + 8r2 = -16r + 16r

Combine like terms: -16r + 16r = 0
-24 + 16r + 8r2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + 2r + r2) = 0

Factor a trinomial.
8((-3 + -1r)(1 + -1r)) = 0

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
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 = {-3, 1}