9r^2-18r=7

Solution for 9r^2-18r=7 equation:

Simplifying
9r2 + -18r = 7

Reorder the terms:
-18r + 9r2 = 7

Solving
-18r + 9r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + -18r + 9r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -18r + 9r2 = 0

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

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

Simplifying
-1 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve:

Simplifying
7 + -3r = 0

Solving
7 + -3r = 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 + -3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3r = 0 + -7
-3r = 0 + -7

Combine like terms: 0 + -7 = -7
-3r = -7

Divide each side by '-3'.
r = 2.333333333

Simplifying
r = 2.333333333
Solution
r = {-0.3333333333, 2.333333333}