(r+4)(2r+5)=0

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Solution for (r+4)(2r+5)=0 equation:


Simplifying
(r + 4)(2r + 5) = 0

Reorder the terms:
(4 + r)(2r + 5) = 0

Reorder the terms:
(4 + r)(5 + 2r) = 0

Multiply (4 + r) * (5 + 2r)
(4(5 + 2r) + r(5 + 2r)) = 0
((5 * 4 + 2r * 4) + r(5 + 2r)) = 0
((20 + 8r) + r(5 + 2r)) = 0
(20 + 8r + (5 * r + 2r * r)) = 0
(20 + 8r + (5r + 2r2)) = 0

Combine like terms: 8r + 5r = 13r
(20 + 13r + 2r2) = 0

Solving
20 + 13r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + r)(5 + 2r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + 2r)' equal to zero and attempt to solve: Simplifying 5 + 2r = 0 Solving 5 + 2r = 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 + 2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2r = 0 + -5 2r = 0 + -5 Combine like terms: 0 + -5 = -5 2r = -5 Divide each side by '2'. r = -2.5 Simplifying r = -2.5

Solution

r = {-4, -2.5}

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