7r^2+9=6r+6r^2

Solution for 7r^2+9=6r+6r^2 equation:

Simplifying
7r2 + 9 = 6r + 6r2

Reorder the terms:
9 + 7r2 = 6r + 6r2

Solving
9 + 7r2 = 6r + 6r2

Solving for variable 'r'.

Reorder the terms:
9 + -6r + 7r2 + -6r2 = 6r + 6r2 + -6r + -6r2

Combine like terms: 7r2 + -6r2 = 1r2
9 + -6r + 1r2 = 6r + 6r2 + -6r + -6r2

Reorder the terms:
9 + -6r + 1r2 = 6r + -6r + 6r2 + -6r2

Combine like terms: 6r + -6r = 0
9 + -6r + 1r2 = 0 + 6r2 + -6r2
9 + -6r + 1r2 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
9 + -6r + 1r2 = 0

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

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 '(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
Solution
r = {3, 3}