x^2+9x+23=-2x-5

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Solution for x^2+9x+23=-2x-5 equation:


Simplifying
x2 + 9x + 23 = -2x + -5

Reorder the terms:
23 + 9x + x2 = -2x + -5

Reorder the terms:
23 + 9x + x2 = -5 + -2x

Solving
23 + 9x + x2 = -5 + -2x

Solving for variable 'x'.

Reorder the terms:
23 + 5 + 9x + 2x + x2 = -5 + -2x + 5 + 2x

Combine like terms: 23 + 5 = 28
28 + 9x + 2x + x2 = -5 + -2x + 5 + 2x

Combine like terms: 9x + 2x = 11x
28 + 11x + x2 = -5 + -2x + 5 + 2x

Reorder the terms:
28 + 11x + x2 = -5 + 5 + -2x + 2x

Combine like terms: -5 + 5 = 0
28 + 11x + x2 = 0 + -2x + 2x
28 + 11x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
28 + 11x + x2 = 0

Factor a trinomial.
(7 + x)(4 + x) = 0

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

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

Solution

x = {-7, -4}

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