30=r(r-7)

Solution for 30=r(r-7) equation:

Simplifying
30 = r(r + -7)

Reorder the terms:
30 = r(-7 + r)
30 = (-7 * r + r * r)
30 = (-7r + r2)

Solving
30 = -7r + r2

Solving for variable 'r'.

Reorder the terms:
30 + 7r + -1r2 = -7r + 7r + r2 + -1r2

Combine like terms: -7r + 7r = 0
30 + 7r + -1r2 = 0 + r2 + -1r2
30 + 7r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
30 + 7r + -1r2 = 0

Factor a trinomial.
(10 + -1r)(3 + r) = 0

Subproblem 1
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

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

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

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

Simplifying
r = -3
Solution
r = {10, -3}