10r^2-35=65r

Solution for 10r^2-35=65r equation:

Simplifying
10r2 + -35 = 65r

Reorder the terms:
-35 + 10r2 = 65r

Solving
-35 + 10r2 = 65r

Solving for variable 'r'.

Reorder the terms:
-35 + -65r + 10r2 = 65r + -65r

Combine like terms: 65r + -65r = 0
-35 + -65r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -13r + 2r2) = 0

Factor a trinomial.
5((-1 + -2r)(7 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve:

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 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 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

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

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

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-0.5, 7}