r^2=7r-12

Solution for r^2=7r-12 equation:

Simplifying
r2 = 7r + -12

Reorder the terms:
r2 = -12 + 7r

Solving
r2 = -12 + 7r

Solving for variable 'r'.

Reorder the terms:
12 + -7r + r2 = -12 + 7r + 12 + -7r

Reorder the terms:
12 + -7r + r2 = -12 + 12 + 7r + -7r

Combine like terms: -12 + 12 = 0
12 + -7r + r2 = 0 + 7r + -7r
12 + -7r + r2 = 7r + -7r

Combine like terms: 7r + -7r = 0
12 + -7r + r2 = 0

Factor a trinomial.
(3 + -1r)(4 + -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 '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {3, 4}