8r^2=56r+64

Solution for 8r^2=56r+64 equation:

Simplifying
8r2 = 56r + 64

Reorder the terms:
8r2 = 64 + 56r

Solving
8r2 = 64 + 56r

Solving for variable 'r'.

Reorder the terms:
-64 + -56r + 8r2 = 64 + 56r + -64 + -56r

Reorder the terms:
-64 + -56r + 8r2 = 64 + -64 + 56r + -56r

Combine like terms: 64 + -64 = 0
-64 + -56r + 8r2 = 0 + 56r + -56r
-64 + -56r + 8r2 = 56r + -56r

Combine like terms: 56r + -56r = 0
-64 + -56r + 8r2 = 0

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

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

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

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-1, 8}