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

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

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

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

Combine like terms: 16 + -3 = 13
16(13 + x) = (x + 3)(x + 3)
(13 * 16 + x * 16) = (x + 3)(x + 3)
(208 + 16x) = (x + 3)(x + 3)

Reorder the terms:
208 + 16x = (3 + x)(x + 3)

Reorder the terms:
208 + 16x = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
208 + 16x = (3(3 + x) + x(3 + x))
208 + 16x = ((3 * 3 + x * 3) + x(3 + x))
208 + 16x = ((9 + 3x) + x(3 + x))
208 + 16x = (9 + 3x + (3 * x + x * x))
208 + 16x = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
208 + 16x = (9 + 6x + x2)

Solving
208 + 16x = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
208 + -9 + 16x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 208 + -9 = 199
199 + 16x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 16x + -6x = 10x
199 + 10x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
199 + 10x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
199 + 10x + -1x2 = 0 + 6x + -6x + x2 + -1x2
199 + 10x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
199 + 10x + -1x2 = 0 + x2 + -1x2
199 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
199 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-199 + -10x + x2 = 0

Move the constant term to the right:

Add '199' to each side of the equation.
-199 + -10x + 199 + x2 = 0 + 199

Reorder the terms:
-199 + 199 + -10x + x2 = 0 + 199

Combine like terms: -199 + 199 = 0
0 + -10x + x2 = 0 + 199
-10x + x2 = 0 + 199

Combine like terms: 0 + 199 = 199
-10x + x2 = 199

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 199 + 25

Reorder the terms:
25 + -10x + x2 = 199 + 25

Combine like terms: 199 + 25 = 224
25 + -10x + x2 = 224

Factor a perfect square on the left side:
(x + -5)(x + -5) = 224

Calculate the square root of the right side: 14.966629547

Break this problem into two subproblems by setting 
(x + -5) equal to 14.966629547 and -14.966629547.

Subproblem 1
x + -5 = 14.966629547

Simplifying
x + -5 = 14.966629547

Reorder the terms:
-5 + x = 14.966629547

Solving
-5 + x = 14.966629547

Solving for variable 'x'.

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 = 14.966629547 + 5

Combine like terms: -5 + 5 = 0
0 + x = 14.966629547 + 5
x = 14.966629547 + 5

Combine like terms: 14.966629547 + 5 = 19.966629547
x = 19.966629547

Simplifying
x = 19.966629547

Subproblem 2
x + -5 = -14.966629547

Simplifying
x + -5 = -14.966629547

Reorder the terms:
-5 + x = -14.966629547

Solving
-5 + x = -14.966629547

Solving for variable 'x'.

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 = -14.966629547 + 5

Combine like terms: -5 + 5 = 0
0 + x = -14.966629547 + 5
x = -14.966629547 + 5

Combine like terms: -14.966629547 + 5 = -9.966629547
x = -9.966629547

Simplifying
x = -9.966629547

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.966629547, -9.966629547}