(x+6)(x+6)+14(x+6)+45=0

Solution for (x+6)(x+6)+14(x+6)+45=0 equation:

Simplifying
(x + 6)(x + 6) + 14(x + 6) + 45 = 0

Reorder the terms:
(6 + x)(x + 6) + 14(x + 6) + 45 = 0

Reorder the terms:
(6 + x)(6 + x) + 14(x + 6) + 45 = 0

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) + 14(x + 6) + 45 = 0
((6 * 6 + x * 6) + x(6 + x)) + 14(x + 6) + 45 = 0
((36 + 6x) + x(6 + x)) + 14(x + 6) + 45 = 0
(36 + 6x + (6 * x + x * x)) + 14(x + 6) + 45 = 0
(36 + 6x + (6x + x2)) + 14(x + 6) + 45 = 0

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) + 14(x + 6) + 45 = 0

Reorder the terms:
36 + 12x + x2 + 14(6 + x) + 45 = 0
36 + 12x + x2 + (6 * 14 + x * 14) + 45 = 0
36 + 12x + x2 + (84 + 14x) + 45 = 0

Reorder the terms:
36 + 84 + 45 + 12x + 14x + x2 = 0

Combine like terms: 36 + 84 = 120
120 + 45 + 12x + 14x + x2 = 0

Combine like terms: 120 + 45 = 165
165 + 12x + 14x + x2 = 0

Combine like terms: 12x + 14x = 26x
165 + 26x + x2 = 0

Solving
165 + 26x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + x)(11 + x) = 0

Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Solution
x = {-15, -11}