14r^2-34r-5-7r^2=0

Solution for 14r^2-34r-5-7r^2=0 equation:

Simplifying
14r2 + -34r + -5 + -7r2 = 0

Reorder the terms:
-5 + -34r + 14r2 + -7r2 = 0

Combine like terms: 14r2 + -7r2 = 7r2
-5 + -34r + 7r2 = 0

Solving
-5 + -34r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -7r)(5 + -1r) = 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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.1428571429, 5}