7r^2+7r-294=0

Solution for 7r^2+7r-294=0 equation:

Simplifying
7r2 + 7r + -294 = 0

Reorder the terms:
-294 + 7r + 7r2 = 0

Solving
-294 + 7r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-42 + r + r2) = 0

Factor a trinomial.
7((-7 + -1r)(6 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
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
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 = {-7, 6}