7r^2-105=14r

Solution for 7r^2-105=14r equation:

Simplifying
7r2 + -105 = 14r

Reorder the terms:
-105 + 7r2 = 14r

Solving
-105 + 7r2 = 14r

Solving for variable 'r'.

Reorder the terms:
-105 + -14r + 7r2 = 14r + -14r

Combine like terms: 14r + -14r = 0
-105 + -14r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-15 + -2r + r2) = 0

Factor a trinomial.
7((-3 + -1r)(5 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
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 = {-3, 5}