5r^2=-30+35r

Solution for 5r^2=-30+35r equation:

Simplifying
5r2 = -30 + 35r

Solving
5r2 = -30 + 35r

Solving for variable 'r'.

Reorder the terms:
30 + -35r + 5r2 = -30 + 35r + 30 + -35r

Reorder the terms:
30 + -35r + 5r2 = -30 + 30 + 35r + -35r

Combine like terms: -30 + 30 = 0
30 + -35r + 5r2 = 0 + 35r + -35r
30 + -35r + 5r2 = 35r + -35r

Combine like terms: 35r + -35r = 0
30 + -35r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -7r + r2) = 0

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

Ignore the factor 5.
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 '(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 = {1, 6}