(x+5)(2x+3)=-5

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Solution for (x+5)(2x+3)=-5 equation:


Simplifying
(x + 5)(2x + 3) = -5

Reorder the terms:
(5 + x)(2x + 3) = -5

Reorder the terms:
(5 + x)(3 + 2x) = -5

Multiply (5 + x) * (3 + 2x)
(5(3 + 2x) + x(3 + 2x)) = -5
((3 * 5 + 2x * 5) + x(3 + 2x)) = -5
((15 + 10x) + x(3 + 2x)) = -5
(15 + 10x + (3 * x + 2x * x)) = -5
(15 + 10x + (3x + 2x2)) = -5

Combine like terms: 10x + 3x = 13x
(15 + 13x + 2x2) = -5

Solving
15 + 13x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
15 + 5 + 13x + 2x2 = -5 + 5

Combine like terms: 15 + 5 = 20
20 + 13x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
20 + 13x + 2x2 = 0

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

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

Solution

x = {-4, -2.5}

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