(2x+1)(x-1)=42

Solution for (2x+1)(x-1)=42 equation:

Simplifying
(2x + 1)(x + -1) = 42

Reorder the terms:
(1 + 2x)(x + -1) = 42

Reorder the terms:
(1 + 2x)(-1 + x) = 42

Multiply (1 + 2x) * (-1 + x)
(1(-1 + x) + 2x * (-1 + x)) = 42
((-1 * 1 + x * 1) + 2x * (-1 + x)) = 42
((-1 + 1x) + 2x * (-1 + x)) = 42
(-1 + 1x + (-1 * 2x + x * 2x)) = 42
(-1 + 1x + (-2x + 2x2)) = 42

Combine like terms: 1x + -2x = -1x
(-1 + -1x + 2x2) = 42

Solving
-1 + -1x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-1 + -42 + -1x + 2x2 = 42 + -42

Combine like terms: -1 + -42 = -43
-43 + -1x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-43 + -1x + 2x2 = 0

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

Divide each side by '2'.
-21.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '21.5' to each side of the equation.
-21.5 + -0.5x + 21.5 + x2 = 0 + 21.5

Reorder the terms:
-21.5 + 21.5 + -0.5x + x2 = 0 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + -0.5x + x2 = 0 + 21.5
-0.5x + x2 = 0 + 21.5

Combine like terms: 0 + 21.5 = 21.5
-0.5x + x2 = 21.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 21.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 21.5 + 0.0625

Combine like terms: 21.5 + 0.0625 = 21.5625
0.0625 + -0.5x + x2 = 21.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 21.5625

Calculate the square root of the right side: 4.643543905

Break this problem into two subproblems by setting 
(x + -0.25) equal to 4.643543905 and -4.643543905.

Subproblem 1
x + -0.25 = 4.643543905

Simplifying
x + -0.25 = 4.643543905

Reorder the terms:
-0.25 + x = 4.643543905

Solving
-0.25 + x = 4.643543905

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 4.643543905 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 4.643543905 + 0.25
x = 4.643543905 + 0.25

Combine like terms: 4.643543905 + 0.25 = 4.893543905
x = 4.893543905

Simplifying
x = 4.893543905

Subproblem 2
x + -0.25 = -4.643543905

Simplifying
x + -0.25 = -4.643543905

Reorder the terms:
-0.25 + x = -4.643543905

Solving
-0.25 + x = -4.643543905

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -4.643543905 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -4.643543905 + 0.25
x = -4.643543905 + 0.25

Combine like terms: -4.643543905 + 0.25 = -4.393543905
x = -4.393543905

Simplifying
x = -4.393543905

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.893543905, -4.393543905}