r(r+3)+6(r+6)=

Solution for r(r+3)+6(r+6)= equation:

Simplifying
r(r + 3) + 6(r + 6) = 0

Reorder the terms:
r(3 + r) + 6(r + 6) = 0
(3 * r + r * r) + 6(r + 6) = 0
(3r + r2) + 6(r + 6) = 0

Reorder the terms:
3r + r2 + 6(6 + r) = 0
3r + r2 + (6 * 6 + r * 6) = 0
3r + r2 + (36 + 6r) = 0

Reorder the terms:
36 + 3r + 6r + r2 = 0

Combine like terms: 3r + 6r = 9r
36 + 9r + r2 = 0

Solving
36 + 9r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 9r + -36 + r2 = 0 + -36

Reorder the terms:
36 + -36 + 9r + r2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 9r + r2 = 0 + -36
9r + r2 = 0 + -36

Combine like terms: 0 + -36 = -36
9r + r2 = -36

The r term is 9r.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9r + 20.25 + r2 = -36 + 20.25

Reorder the terms:
20.25 + 9r + r2 = -36 + 20.25

Combine like terms: -36 + 20.25 = -15.75
20.25 + 9r + r2 = -15.75

Factor a perfect square on the left side:
(r + 4.5)(r + 4.5) = -15.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.