x^2+12x+21=-6

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Solution for x^2+12x+21=-6 equation:


Simplifying
x2 + 12x + 21 = -6

Reorder the terms:
21 + 12x + x2 = -6

Solving
21 + 12x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
21 + 6 + 12x + x2 = -6 + 6

Combine like terms: 21 + 6 = 27
27 + 12x + x2 = -6 + 6

Combine like terms: -6 + 6 = 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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