8=r(r-7)

Solution for 8=r(r-7) equation:

Simplifying
8 = r(r + -7)

Reorder the terms:
8 = r(-7 + r)
8 = (-7 * r + r * r)
8 = (-7r + r2)

Solving
8 = -7r + r2

Solving for variable 'r'.

Reorder the terms:
8 + 7r + -1r2 = -7r + 7r + r2 + -1r2

Combine like terms: -7r + 7r = 0
8 + 7r + -1r2 = 0 + r2 + -1r2
8 + 7r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
8 + 7r + -1r2 = 0

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

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

Simplifying
1 + r = 0

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

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

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

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