(x+3)(x+3)-16=0

Solution for (x+3)(x+3)-16=0 equation:

Simplifying
(x + 3)(x + 3) + -16 = 0

Reorder the terms:
(3 + x)(x + 3) + -16 = 0

Reorder the terms:
(3 + x)(3 + x) + -16 = 0

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) + -16 = 0
((3 * 3 + x * 3) + x(3 + x)) + -16 = 0
((9 + 3x) + x(3 + x)) + -16 = 0
(9 + 3x + (3 * x + x * x)) + -16 = 0
(9 + 3x + (3x + x2)) + -16 = 0

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) + -16 = 0

Reorder the terms:
9 + -16 + 6x + x2 = 0

Combine like terms: 9 + -16 = -7
-7 + 6x + x2 = 0

Solving
-7 + 6x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-7, 1}