3x+5=2(2x-1)*(x-3)

Solution for 3x+5=2(2x-1)*(x-3) equation:

Simplifying
3x + 5 = 2(2x + -1)(x + -3)

Reorder the terms:
5 + 3x = 2(2x + -1)(x + -3)

Reorder the terms:
5 + 3x = 2(-1 + 2x)(x + -3)

Reorder the terms:
5 + 3x = 2(-1 + 2x)(-3 + x)

Multiply (-1 + 2x) * (-3 + x)
5 + 3x = 2(-1(-3 + x) + 2x * (-3 + x))
5 + 3x = 2((-3 * -1 + x * -1) + 2x * (-3 + x))
5 + 3x = 2((3 + -1x) + 2x * (-3 + x))
5 + 3x = 2(3 + -1x + (-3 * 2x + x * 2x))
5 + 3x = 2(3 + -1x + (-6x + 2x2))

Combine like terms: -1x + -6x = -7x
5 + 3x = 2(3 + -7x + 2x2)
5 + 3x = (3 * 2 + -7x * 2 + 2x2 * 2)
5 + 3x = (6 + -14x + 4x2)

Solving
5 + 3x = 6 + -14x + 4x2

Solving for variable 'x'.

Reorder the terms:
5 + -6 + 3x + 14x + -4x2 = 6 + -14x + 4x2 + -6 + 14x + -4x2

Combine like terms: 5 + -6 = -1
-1 + 3x + 14x + -4x2 = 6 + -14x + 4x2 + -6 + 14x + -4x2

Combine like terms: 3x + 14x = 17x
-1 + 17x + -4x2 = 6 + -14x + 4x2 + -6 + 14x + -4x2

Reorder the terms:
-1 + 17x + -4x2 = 6 + -6 + -14x + 14x + 4x2 + -4x2

Combine like terms: 6 + -6 = 0
-1 + 17x + -4x2 = 0 + -14x + 14x + 4x2 + -4x2
-1 + 17x + -4x2 = -14x + 14x + 4x2 + -4x2

Combine like terms: -14x + 14x = 0
-1 + 17x + -4x2 = 0 + 4x2 + -4x2
-1 + 17x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-1 + 17x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -4.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -4.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -4.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -4.25x + x2 = 0 + -0.25
-4.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-4.25x + x2 = -0.25

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -0.25 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -0.25 + 4.515625

Combine like terms: -0.25 + 4.515625 = 4.265625
4.515625 + -4.25x + x2 = 4.265625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 4.265625

Calculate the square root of the right side: 2.065338955

Break this problem into two subproblems by setting 
(x + -2.125) equal to 2.065338955 and -2.065338955.

Subproblem 1
x + -2.125 = 2.065338955

Simplifying
x + -2.125 = 2.065338955

Reorder the terms:
-2.125 + x = 2.065338955

Solving
-2.125 + x = 2.065338955

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = 2.065338955 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 2.065338955 + 2.125
x = 2.065338955 + 2.125

Combine like terms: 2.065338955 + 2.125 = 4.190338955
x = 4.190338955

Simplifying
x = 4.190338955

Subproblem 2
x + -2.125 = -2.065338955

Simplifying
x + -2.125 = -2.065338955

Reorder the terms:
-2.125 + x = -2.065338955

Solving
-2.125 + x = -2.065338955

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = -2.065338955 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -2.065338955 + 2.125
x = -2.065338955 + 2.125

Combine like terms: -2.065338955 + 2.125 = 0.059661045
x = 0.059661045

Simplifying
x = 0.059661045

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.190338955, 0.059661045}