(x+1)(2x+5)=0

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Solution for (x+1)(2x+5)=0 equation:


Simplifying
(x + 1)(2x + 5) = 0

Reorder the terms:
(1 + x)(2x + 5) = 0

Reorder the terms:
(1 + x)(5 + 2x) = 0

Multiply (1 + x) * (5 + 2x)
(1(5 + 2x) + x(5 + 2x)) = 0
((5 * 1 + 2x * 1) + x(5 + 2x)) = 0
((5 + 2x) + x(5 + 2x)) = 0
(5 + 2x + (5 * x + 2x * x)) = 0
(5 + 2x + (5x + 2x2)) = 0

Combine like terms: 2x + 5x = 7x
(5 + 7x + 2x2) = 0

Solving
5 + 7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + 2x)(1 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-2.5, -1}

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