(x+3)*(x+3)+9*(x+3)+14=0

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Solution for (x+3)*(x+3)+9*(x+3)+14=0 equation: 


Simplifying
(x + 3)(x + 3) + 9(x + 3) + 14 = 0

Reorder the terms:
(3 + x)(x + 3) + 9(x + 3) + 14 = 0

Reorder the terms:
(3 + x)(3 + x) + 9(x + 3) + 14 = 0

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) + 9(x + 3) + 14 = 0
((3 * 3 + x * 3) + x(3 + x)) + 9(x + 3) + 14 = 0
((9 + 3x) + x(3 + x)) + 9(x + 3) + 14 = 0
(9 + 3x + (3 * x + x * x)) + 9(x + 3) + 14 = 0
(9 + 3x + (3x + x2)) + 9(x + 3) + 14 = 0

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) + 9(x + 3) + 14 = 0

Reorder the terms:
9 + 6x + x2 + 9(3 + x) + 14 = 0
9 + 6x + x2 + (3 * 9 + x * 9) + 14 = 0
9 + 6x + x2 + (27 + 9x) + 14 = 0

Reorder the terms:
9 + 27 + 14 + 6x + 9x + x2 = 0

Combine like terms: 9 + 27 = 36
36 + 14 + 6x + 9x + x2 = 0

Combine like terms: 36 + 14 = 50
50 + 6x + 9x + x2 = 0

Combine like terms: 6x + 9x = 15x
50 + 15x + x2 = 0

Solving
50 + 15x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + x)(5 + x) = 0


Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-10, -5}

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