35r^2-65r+2=-6-4r

Solution for 35r^2-65r+2=-6-4r equation:

Simplifying
35r2 + -65r + 2 = -6 + -4r

Reorder the terms:
2 + -65r + 35r2 = -6 + -4r

Solving
2 + -65r + 35r2 = -6 + -4r

Solving for variable 'r'.

Reorder the terms:
2 + 6 + -65r + 4r + 35r2 = -6 + -4r + 6 + 4r

Combine like terms: 2 + 6 = 8
8 + -65r + 4r + 35r2 = -6 + -4r + 6 + 4r

Combine like terms: -65r + 4r = -61r
8 + -61r + 35r2 = -6 + -4r + 6 + 4r

Reorder the terms:
8 + -61r + 35r2 = -6 + 6 + -4r + 4r

Combine like terms: -6 + 6 = 0
8 + -61r + 35r2 = 0 + -4r + 4r
8 + -61r + 35r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
8 + -61r + 35r2 = 0

Factor a trinomial.
(1 + -7r)(8 + -5r) = 0

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

Simplifying
1 + -7r = 0

Solving
1 + -7r = 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 + -7r = 0 + -1

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

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

Divide each side by '-7'.
r = 0.1428571429

Simplifying
r = 0.1428571429
Subproblem 2
Set the factor '(8 + -5r)' equal to zero and attempt to solve:

Simplifying
8 + -5r = 0

Solving
8 + -5r = 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 + -5r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5r = 0 + -8
-5r = 0 + -8

Combine like terms: 0 + -8 = -8
-5r = -8

Divide each side by '-5'.
r = 1.6

Simplifying
r = 1.6
Solution
r = {0.1428571429, 1.6}