x(x+4)+5=-1-(2x+3)

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Solution for x(x+4)+5=-1-(2x+3) equation:


Simplifying
x(x + 4) + 5 = -1 + -1(2x + 3)

Reorder the terms:
x(4 + x) + 5 = -1 + -1(2x + 3)
(4 * x + x * x) + 5 = -1 + -1(2x + 3)
(4x + x2) + 5 = -1 + -1(2x + 3)

Reorder the terms:
5 + 4x + x2 = -1 + -1(2x + 3)

Reorder the terms:
5 + 4x + x2 = -1 + -1(3 + 2x)
5 + 4x + x2 = -1 + (3 * -1 + 2x * -1)
5 + 4x + x2 = -1 + (-3 + -2x)

Combine like terms: -1 + -3 = -4
5 + 4x + x2 = -4 + -2x

Solving
5 + 4x + x2 = -4 + -2x

Solving for variable 'x'.

Reorder the terms:
5 + 4 + 4x + 2x + x2 = -4 + -2x + 4 + 2x

Combine like terms: 5 + 4 = 9
9 + 4x + 2x + x2 = -4 + -2x + 4 + 2x

Combine like terms: 4x + 2x = 6x
9 + 6x + x2 = -4 + -2x + 4 + 2x

Reorder the terms:
9 + 6x + x2 = -4 + 4 + -2x + 2x

Combine like terms: -4 + 4 = 0
9 + 6x + x2 = 0 + -2x + 2x
9 + 6x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
9 + 6x + x2 = 0

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

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-3, -3}

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