x^2+9x=-27-3x

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Solution for x^2+9x=-27-3x equation:


Simplifying
x2 + 9x = -27 + -3x

Reorder the terms:
9x + x2 = -27 + -3x

Solving
9x + x2 = -27 + -3x

Solving for variable 'x'.

Reorder the terms:
27 + 9x + 3x + x2 = -27 + -3x + 27 + 3x

Combine like terms: 9x + 3x = 12x
27 + 12x + x2 = -27 + -3x + 27 + 3x

Reorder the terms:
27 + 12x + x2 = -27 + 27 + -3x + 3x

Combine like terms: -27 + 27 = 0
27 + 12x + x2 = 0 + -3x + 3x
27 + 12x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
27 + 12x + x2 = 0

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

Subproblem 1

Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9

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 = {-9, -3}

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