r^2+14r-9=6

Solution for r^2+14r-9=6 equation:

Simplifying
r2 + 14r + -9 = 6

Reorder the terms:
-9 + 14r + r2 = 6

Solving
-9 + 14r + r2 = 6

Solving for variable 'r'.

Reorder the terms:
-9 + -6 + 14r + r2 = 6 + -6

Combine like terms: -9 + -6 = -15
-15 + 14r + r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-15 + 14r + r2 = 0

Factor a trinomial.
(-15 + -1r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-15 + -1r)' equal to zero and attempt to solve:

Simplifying
-15 + -1r = 0

Solving
-15 + -1r = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1r = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1r = 0 + 15
-1r = 0 + 15

Combine like terms: 0 + 15 = 15
-1r = 15

Divide each side by '-1'.
r = -15

Simplifying
r = -15
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-15, 1}