r^2+12r=45

Solution for r^2+12r=45 equation:

Simplifying
r2 + 12r = 45

Reorder the terms:
12r + r2 = 45

Solving
12r + r2 = 45

Solving for variable 'r'.

Reorder the terms:
-45 + 12r + r2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 12r + r2 = 0

Factor a trinomial.
(-15 + -1r)(3 + -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 '(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 = {-15, 3}