(2x+1)(x-16)=(3x-2)(x+3)

Solution for (2x+1)(x-16)=(3x-2)(x+3) equation:

Simplifying
(2x + 1)(x + -16) = (3x + -2)(x + 3)

Reorder the terms:
(1 + 2x)(x + -16) = (3x + -2)(x + 3)

Reorder the terms:
(1 + 2x)(-16 + x) = (3x + -2)(x + 3)

Multiply (1 + 2x) * (-16 + x)
(1(-16 + x) + 2x * (-16 + x)) = (3x + -2)(x + 3)
((-16 * 1 + x * 1) + 2x * (-16 + x)) = (3x + -2)(x + 3)
((-16 + 1x) + 2x * (-16 + x)) = (3x + -2)(x + 3)
(-16 + 1x + (-16 * 2x + x * 2x)) = (3x + -2)(x + 3)
(-16 + 1x + (-32x + 2x2)) = (3x + -2)(x + 3)

Combine like terms: 1x + -32x = -31x
(-16 + -31x + 2x2) = (3x + -2)(x + 3)

Reorder the terms:
-16 + -31x + 2x2 = (-2 + 3x)(x + 3)

Reorder the terms:
-16 + -31x + 2x2 = (-2 + 3x)(3 + x)

Multiply (-2 + 3x) * (3 + x)
-16 + -31x + 2x2 = (-2(3 + x) + 3x * (3 + x))
-16 + -31x + 2x2 = ((3 * -2 + x * -2) + 3x * (3 + x))
-16 + -31x + 2x2 = ((-6 + -2x) + 3x * (3 + x))
-16 + -31x + 2x2 = (-6 + -2x + (3 * 3x + x * 3x))
-16 + -31x + 2x2 = (-6 + -2x + (9x + 3x2))

Combine like terms: -2x + 9x = 7x
-16 + -31x + 2x2 = (-6 + 7x + 3x2)

Solving
-16 + -31x + 2x2 = -6 + 7x + 3x2

Solving for variable 'x'.

Reorder the terms:
-16 + 6 + -31x + -7x + 2x2 + -3x2 = -6 + 7x + 3x2 + 6 + -7x + -3x2

Combine like terms: -16 + 6 = -10
-10 + -31x + -7x + 2x2 + -3x2 = -6 + 7x + 3x2 + 6 + -7x + -3x2

Combine like terms: -31x + -7x = -38x
-10 + -38x + 2x2 + -3x2 = -6 + 7x + 3x2 + 6 + -7x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-10 + -38x + -1x2 = -6 + 7x + 3x2 + 6 + -7x + -3x2

Reorder the terms:
-10 + -38x + -1x2 = -6 + 6 + 7x + -7x + 3x2 + -3x2

Combine like terms: -6 + 6 = 0
-10 + -38x + -1x2 = 0 + 7x + -7x + 3x2 + -3x2
-10 + -38x + -1x2 = 7x + -7x + 3x2 + -3x2

Combine like terms: 7x + -7x = 0
-10 + -38x + -1x2 = 0 + 3x2 + -3x2
-10 + -38x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-10 + -38x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 38x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + 38x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 38x + x2 = 0

Solving
10 + 38x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 38x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 38x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 38x + x2 = 0 + -10
38x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
38x + x2 = -10

The x term is 38x.  Take half its coefficient (19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
38x + 361 + x2 = -10 + 361

Reorder the terms:
361 + 38x + x2 = -10 + 361

Combine like terms: -10 + 361 = 351
361 + 38x + x2 = 351

Factor a perfect square on the left side:
(x + 19)(x + 19) = 351

Calculate the square root of the right side: 18.734993995

Break this problem into two subproblems by setting 
(x + 19) equal to 18.734993995 and -18.734993995.

Subproblem 1
x + 19 = 18.734993995

Simplifying
x + 19 = 18.734993995

Reorder the terms:
19 + x = 18.734993995

Solving
19 + x = 18.734993995

Solving for variable 'x'.

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

Add '-19' to each side of the equation.
19 + -19 + x = 18.734993995 + -19

Combine like terms: 19 + -19 = 0
0 + x = 18.734993995 + -19
x = 18.734993995 + -19

Combine like terms: 18.734993995 + -19 = -0.265006005
x = -0.265006005

Simplifying
x = -0.265006005

Subproblem 2
x + 19 = -18.734993995

Simplifying
x + 19 = -18.734993995

Reorder the terms:
19 + x = -18.734993995

Solving
19 + x = -18.734993995

Solving for variable 'x'.

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

Add '-19' to each side of the equation.
19 + -19 + x = -18.734993995 + -19

Combine like terms: 19 + -19 = 0
0 + x = -18.734993995 + -19
x = -18.734993995 + -19

Combine like terms: -18.734993995 + -19 = -37.734993995
x = -37.734993995

Simplifying
x = -37.734993995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.265006005, -37.734993995}
Solution
x = {-0.265006005, -37.734993995}