(r+6)(r+3)=-2

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Solution for (r+6)(r+3)=-2 equation:


Simplifying
(r + 6)(r + 3) = -2

Reorder the terms:
(6 + r)(r + 3) = -2

Reorder the terms:
(6 + r)(3 + r) = -2

Multiply (6 + r) * (3 + r)
(6(3 + r) + r(3 + r)) = -2
((3 * 6 + r * 6) + r(3 + r)) = -2
((18 + 6r) + r(3 + r)) = -2
(18 + 6r + (3 * r + r * r)) = -2
(18 + 6r + (3r + r2)) = -2

Combine like terms: 6r + 3r = 9r
(18 + 9r + r2) = -2

Solving
18 + 9r + r2 = -2

Solving for variable 'r'.

Reorder the terms:
18 + 2 + 9r + r2 = -2 + 2

Combine like terms: 18 + 2 = 20
20 + 9r + r2 = -2 + 2

Combine like terms: -2 + 2 = 0
20 + 9r + r2 = 0

Factor a trinomial.
(5 + r)(4 + r) = 0

Subproblem 1

Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5

Subproblem 2

Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 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 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4

Solution

r = {-5, -4}

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