(2x+5)(x+1)=-1

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Solution for (2x+5)(x+1)=-1 equation:


Simplifying
(2x + 5)(x + 1) = -1

Reorder the terms:
(5 + 2x)(x + 1) = -1

Reorder the terms:
(5 + 2x)(1 + x) = -1

Multiply (5 + 2x) * (1 + x)
(5(1 + x) + 2x * (1 + x)) = -1
((1 * 5 + x * 5) + 2x * (1 + x)) = -1
((5 + 5x) + 2x * (1 + x)) = -1
(5 + 5x + (1 * 2x + x * 2x)) = -1
(5 + 5x + (2x + 2x2)) = -1

Combine like terms: 5x + 2x = 7x
(5 + 7x + 2x2) = -1

Solving
5 + 7x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
5 + 1 + 7x + 2x2 = -1 + 1

Combine like terms: 5 + 1 = 6
6 + 7x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
6 + 7x + 2x2 = 0

Factor a trinomial.
(2 + x)(3 + 2x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {-2, -1.5}

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